ORIGINAL_ARTICLE
Normalized laplacian spectrum of two new types of join graphs
Let $G$ be a graph without an isolated vertex, the normalized Laplacian matrix $\tilde{\mathcal{L}}(G)$ is defined as $\tilde{\mathcal{L}}(G)=\mathcal{D}^{-\frac{1}{2}}\mathcal{L}(G)\mathcal{D}^{-\frac{1}{2}}$, where $\mathcal{D}$ is a diagonal matrix whose entries are degree of vertices of $G$. The eigenvalues of $\tilde{\mathcal{L}}(G)$ are called as the normalized Laplacian eigenvalues of $G$. In this paper, we obtain the normalized Laplacian spectrum of two new types of join graphs. In continuing, we determine the integrality of normalized Laplacian eigenvalues of graphs. Finally, the normalized Laplacian energy and degree Kirchhoff index of these new graph products are derived.
http://jlta.iauctb.ac.ir/article_530214_bbc846be4c0a7da114894aa6723fc11b.pdf
2017-06-01T11:23:20
2017-10-23T11:23:20
1
9
join of graphs
normalized Laplacian eigenvalue
integral eigenvalue
M.
Hakimi-Nezhaad
m.hakimi20@gmail.com
true
1
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
AUTHOR
M.
Ghorbani
mghorbani@srttu.edu
true
2
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
LEAD_AUTHOR
[1] A. E. Brouwer, W. H. Haemers, Spectra of Graphs, Universitext, Springer, New York, 2012.
1
[2] S. Butler, Eigenvalues and Structures of Graphs, Ph.D. dissertation, University of California, San Diego, 2008.
2
[3] M. Cavers, The normalized Laplacian matrix and general Randic index of graphs, Ph.D. University of Regina, 2010.
3
[4] M. Cavers, S. Fallat, S. Kirkland, On the normalized Laplacian energy and general Randic index R-1 of graphs, Linear Algebra Appl. 433 (2010), 172-190.
4
[5] H. Chen, F. Zhang, Resistance distance and the normalized Laplacian spectrum, Discr. Appl. Math. 155 (2007), 654-661.
5
[6] F. R. K. Chung, Spectral Graph Theory, American Math. Soc. Providence, 1997.
6
[7] D. Cvetkovic, M. Doob, H. Sachs, Spectra of Graphs: Theory and Applications, Academic Press, New York, 1980.
7
[8] I. Gutman, The energy of a graph, Steiermrkisches Mathematisches Symposium (Stift Rein, Graz, 1978), Ber. Math. Statist. Sekt. Forsch. Graz 103 (1978) 1-22.
8
[9] I. Gutman, B. Mohar, The Quasi-Wiener and the Kirchho indicescoincide, J. Chem. Inf. Comput. Sci. 36 (1996), 982-985.
9
[10] I. Gutman, The energy of a graph: old and new results, in: A. Betten, A. Kohner, R. Laue, A. Wassermann (Eds.), Algebraic Combinatorics and Applications, Springer, Berlin, 2001, 196-211.
10
[11] M. Hakimi-Nezhaad, A. R. Ashra, I. Gutman, Note on degree Kirchho index of graphs, Trans. Comb. 2 (3) (2013), 43-52.
11
[12] M. Hakimi-Nezhaad, A. R. Ashra, A note on normalized Laplacian energy of graphs, J. Contemp. Math. Anal. 49 (5) (2014), 207-211.
12
[13] G. Indulal, Spectrum of two new joins of graphs and innite families of integral graphs, Kragujevac J. Math. 36 (1) (2012), 133-139.
13
[14] E. R. Van Dam, G. R. Omidi, Graphs whose normalized Laplacian has three eigenvalues, Linear Algebra Appl. 435 (10) (2011), 2560-2569.
14
[15] M. R. Jooyandeh, D. Kiani, M. Mirzakhah, Incidence energy of a graph, MATCH Commun. Math. Comput. Chem. 62 (2009), 561-572.
15
[16] D. J. Klein, M. Randic, Resistance distance, J. Math. Chem. 12 (1993), 81-95.
16
[17] X. Li, Y. Shi, I. Gutman, Graph energy, Springer, New York, 2012.
17
[18] B. Zhou, N. Trinajstic, On resistance-distance and Kirchho index, J. Math. Chem. 46 (2009), 283-289.
18
ORIGINAL_ARTICLE
The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented and results are compared to the analytical solution and Triangular functions (TF), Delta basis functions (DFs), block-pulse functions , sinc fucntions, Adomian decomposition, computational, Haar wavelet and direct methods to demonstrate the validity and applicability of the proposed method.
http://jlta.iauctb.ac.ir/article_530220_dff904fa08b1056450c1a5a5977c0379.pdf
2017-06-01T11:23:20
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11
28
Radial basis functions
Fredholm integral equations system
J.
Nazari
jinoosnazari@yahoo.com
true
1
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
LEAD_AUTHOR
M.
Nili Ahmadabadi
mneely59@hotmail.com
true
2
Department of Mathematics, Najafabad Branch, Islamic Azad University,
Najafabad, Iran
Department of Mathematics, Najafabad Branch, Islamic Azad University,
Najafabad, Iran
Department of Mathematics, Najafabad Branch, Islamic Azad University,
Najafabad, Iran
AUTHOR
H.
Almasieh
true
3
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
AUTHOR
[1] H. Almasieh, J. N. Meleh, A meshless method for the numerical solution of nonlinear Volterra - Fredholm integro-differential equations using radial basis functions. International Conference on Mathematical Sciences & computer Engineering (ICMSCE 2012).
1
[2] H. Almasieh, J. N. Meleh, Hybrid functions method based on radial basis functions for solving nonlinear Fredholm integrad equations. Journal of Mathematical Extention, 7 (3) (2013), 29-38.
2
[3] H. Almasieh, J. N. Meleh, Numerical solution of a class of mixed two- dimensional nonlinear VolterraFredholm integral equations using multiquadric radial basis functions. J. Comput. Appl. Math., 260 (2014), 173-179.
3
[4] H. Almasieh, M. Roodaki, Triangular functions method for the solution of Fredholm integral equations system. Ain Shams Engineering Journal 3 (2012), 411-416.
4
[5] K. E. Atkinson, The numerical solution of integral equations of the second kind. Cambridge University Press, Cambridge, 1997.
5
[6] E. Babolian, Z. Mansouri, A. Hatamzadeh-Varmarzgar, A direct method for numerically solving integral equations systems using orthogonal traingular functions. International Journal of Industrial Mathematics 1 (2) (2009), 135-145.
6
[7] E. Babolian, J. Biazar, A. R. Vahidi, The decomposition method applied to systems of Fredholm integral equations of the second kind. Appl. Math. Comput. 148 (2004), 443-52.
7
[8] A. H.-D. Cheng, M. A. Golberg, E. J. Kansa, G. Zammito, Exponential convergence and H-C multiquadric collocation method for partial differential equations. Numer. Meth. Partial. Dier. Equa., 19 (5) (2003), 571-594.
8
[9] L. M. Delves, J. L. Mohammed, Computational methods for integral equations. Cambridge University Press, 1985.
9
[10] M. C. De Bonis, C. Laurita, Numerical treatment of second kind integral equation systems on bounded intervals. J. Comput. Appl. Math. 217 (2008), 67-87.
10
[11] K. Maleknejad, M. Shahrezaee, H. Khatami, Numerical solution of integral equations system of the second kind by blockpulse functions. Appl. Math. Comput., 166 (1) (2005), 15-24.
11
[12] O. M. Ogunlaran, O. F. Akinlotan, A computational method for system of linear Fredholm integral equations Mathematical Theory and Modeling 3 (4) (2013), 1-6.
12
[13] K. Parand, J. A. Rad, Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis funetions. Appl. Math. Comput., 218 (2012), 5292-5309.
13
[14] J. Rashidinia, M. Zarebnia, Convergence of approximate solution of system of Fredholm integral equations.J. Math. Anal. Appl., 333 (2007), 1216-1227.
14
[15] M. Roodaki, H. Almasieh, Delta basis functions and their applications to systems of integral equations. Comput. Math. Appl. 63 (1) (2012), 100-109.
15
[16] A. R. Vahidi, M. Mokhtari, On the decomposition method for system of linear Fredholm integral equations of the second kind. Appl. Math. Sci., 2 (2) (2008), 57-62.
16
[17] H. A. Zedan, E. Alaidarous, Haar wavelet method for the system of integral equations. Abstract and Applied Analysis 2014 (2014), 1-9.
17
ORIGINAL_ARTICLE
Unique common coupled fixed point theorem for four maps in $S_b$-metric spaces
In this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $S_b$-metric spaces satisfying a contrctive type condition. We furnish an example to support our main theorem. We also give a corollary for Junck type maps.
http://jlta.iauctb.ac.ir/article_530217_56934be0fc2de05532e4acfcd9699735.pdf
2017-06-01T11:23:20
2017-10-23T11:23:20
29
43
$S_b$-metric space
$w$-compatible pairs
$S_b$-completeness
coupled fixed point
K. P. R.
Rao
kprrao2004@yahoo.com
true
1
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,
Guntur-522 510, Andhra Pradesh, India
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,
Guntur-522 510, Andhra Pradesh, India
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,
Guntur-522 510, Andhra Pradesh, India
LEAD_AUTHOR
G. V. N.
Kishore
kishore.apr2@gmail.com
true
2
Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502,
Andhra Pradesh, India
Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502,
Andhra Pradesh, India
Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502,
Andhra Pradesh, India
AUTHOR
Sk.
Sadik
sadikcrrce@gmail.com
true
3
Department of Mathematics, Sir C R R College of Engineering, Eluru,
West Godavari-534 007, Andhra Pradesh, India
Department of Mathematics, Sir C R R College of Engineering, Eluru,
West Godavari-534 007, Andhra Pradesh, India
Department of Mathematics, Sir C R R College of Engineering, Eluru,
West Godavari-534 007, Andhra Pradesh, India
AUTHOR
[1] M. Abbas, M. Ali khan, S. Randenovic, Common coupled xed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202.
1
[2] S. Czerwik, Contraction mapping in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, 1 (1993), 5-11.
2
[3] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis. Theory, Methods and Applications, 65 (7) (2006), 1379-1393.
3
[4] V. Lakshmikantham, L. Ciric, Coupled xed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis. Theory, Methods and Applications, 70 (12) (2009), 4341-4349.
4
[5] H. Rahimi, P. Vetro, G. Soleimani Rad, Coupled xed point results for T-contractions on cone metric spaces with applications, Math. Notes, 98 (1) (2015), 158-167.
5
[6] H. Rahimi, S. Radenovic, G. Soleimani Rad, Cone metric type space and new coupled xed point theorems, J. Nonlinear. Anal. Optimization (JNAO), 6 (1) (2015), 1-9.
6
[7] S. Sedghi, I. Altun, N. Shobe, M. Salahshour, Some properties of S-metric space and xed point results, Kyung pook Math. J., 54 (2014), 113-122.
7
[8] S. Sedghi, A. Gholidahneh, T. Dosenovic, J. Esfahani, S. Radenovic, Common xed point of four maps in Sb-metric spaces, J. Linear. Topol. Algebra., 5 (2) (2016), 93-104.
8
[9] S. Sedghi, A. Gholidahneh, K. P. R. Rao, Common fixed point of two R- weakly commuting mappings in Sb-metric spaces, Mathematical Science letters (to appear).
9
[10] S. Sedghi, N. Shobe, A. Aliouche, A generalization of xed point theorem in S-metric spaces, Mat. Vesnik, 64 (2012), 258-266.
10
[11] S. Sedghi, N. Shobe, T. Dosenovic, Fixed point results in S-metric spaces, Nonlinear Funct. Anal. Appl., 20 (1) (2015), 55-67.
11
ORIGINAL_ARTICLE
Coupled fixed point theorems involving contractive condition of integral type in generalized metric spaces
In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples. In this manuscript, we prove some coupled fixed point theorems for two pairs of self mappings satisfying contractive conditions of integral type in generalized metric spaces. We furnish suitable illustrative examples.
http://jlta.iauctb.ac.ir/article_530218_9ce6588837690e14ec3335854e50166b.pdf
2017-06-01T11:23:20
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45
53
Generalized metric space
coupled fixed points
integral type contractive mapping
Fixed point
R.
Shah
safeer_rahim@yahoo.com
true
1
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
LEAD_AUTHOR
A.
Zada
true
2
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
AUTHOR
[1] M. Abbas, G. Jungck, Common xed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420.
1
[2] M. Abbas, B. E. Rhoades, Common xed point results for noncommuting mapping without continuity in generalized metric spaces, Appl. Math. Comput. 215 (2009), 262-269.
2
[3] H. Aydi, A xed point theorem for a contractive condition of integral type involving altering distances, Int. J. Nonlinear Anal. Appl., 3 (1) (2012), 42-53.
3
[4] T. Abdeljawad, Completion of cone metric spaces, Hacet. J. Math. Stat., 39 (2010), 67-74.
4
[5] Z. Badehian, M. S. Asgari, Integral type xed point theorems for -admissible mappings satisfying ϕ-contractive inequality, Filomat., 30 (12) (2016), 3227-3234.
5
[6] I. Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theor. Appl., (2006), Article ID 74503. pp. 1-7.
6
[7] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis., 65 (2006), 1379 -1393.
7
[8] A. Branciari, A xed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sciences., 29 (9) (2002), 531-536.
8
[9] L. G. Haung, X. Zhang, Cone metric spaces and xed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1468-1476.
9
[10] G. Jungck, Commuting maps and xed points, Am. Math. Monthly. 83 (1976), 261-263.
10
[11] G. Jungck, Compatible mappings and common xed points, Int. J. Math. Sci. 9 (4) (1986), 771 -779.
11
[12] G. Jungck, Common xed points for commuting and compatible maps on compacta, Proc. Amer. Math. Soc. 103 (1988), 977-983.
12
[13] G. Jungck, N. Hussain, Compatible maps and invariant approximations, J. Math. Anal. Appl. 325 (2) (2007), 1003-1012.
13
[14] V. Lakshmikantham, L. Ciric, Coupled xed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, 70 (2009), 4341-4349.
14
[15] P. P. Murthy, K. Tas, New common xed point theorems of Gregus type for R-weakly commuting mappings in 2-metric spaces, Hacet. J. Math. Stat. 38 (2009), 285 -291.
15
[16] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2) (2006), 289-297.
16
[17] R. P. Pant, Common xed points of noncommuting mappings, J. Math. Anal. Appl., 188 (1994), 436-440.
17
[18] V. Popa, M. Mocanu, Altering distance and common xed points under implicit relations, Hacet. J. Math. Stat. 38 (2009), 329-337.
18
[19] H. Rahimi, P. Vetro, G. Soleimani Rad, Coupled xed-point results for T-contractions on cone metric spaces with applications, Math. Notes. 98 (1) (2015), 158-167.
19
[20] H. Rahimi, G. Soleimani Rad, Fixed point theory in various spaces, Lambert Academic Publishing (LAP), Germany, 2012.
20
[21] R. Shah, A. Zada, Some common xed point theorems of compatible maps with integral type contraction in G-metric spaces, Proceedings of the Institute of Applied Mathematics, 5 (1) (2106), 64-74.
21
[22] R. Shah, A. Zada and T. Li, New common coupled xed point results of integral type contraction in generalized metric spaces, J. Anal. Num. Theor., 4 (2) (2106), 145-152.
22
[23] W. Shatanawi, Coupled xed point theorems in generalized metric spaces, Hacet. J. Math. Stat. 40 (3) (2011), 441-447.
23
[24] A. Zada, R. Shah, T. Li, Integral type contraction and coupled coincidence xed point theorems for two pairs in g-metric spaces, Hacet. J. Math. Stat. 45 (5) (2016), 1475-1484.
24
ORIGINAL_ARTICLE
Characterization of $\delta$-double derivations on rings and algebras
The main purpose of this article is to offer some characterizations of $\delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $\mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,\delta:R\to R$ such that $$d(x^n) =\Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+\Sigma^{n-2}_{k=0} \Sigma^{n-2-k}_{i=0} x^k\delta(x)x^i\delta(x)x^{n-2-k-i}$$ is fulfilled for all $x\in \mathcal{R}$. If $\delta(1) = 0$, then $d$ is a Jordan $\delta$-double derivation. In particular, if $\mathcal{R}$ is a semiprime algebra and further, $\delta^2(x^2) = \delta^2(x)x + x\delta^2(x) + 2(\delta(x))^2$ holds for all $x\in \mathcal{R}$, then $d-\frac{1}{2}\delta^2$ is an ordinary derivation on $\mathcal{R}$.
http://jlta.iauctb.ac.ir/article_530219_27c0141510309a0b0e9c5e4e2896400c.pdf
2017-06-01T11:23:20
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55
65
$delta$-Double derivation
Jordan $delta$-double derivation
$n$-torsion free semiprime ring
A.
Hosseini
hosseini.amin82@gmail.com
true
1
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
LEAD_AUTHOR
[1] D. Bridges and J. Bergen, On the derivation of xn in a ring, Proc. Amer. Math. Soc., 90 (1984), 25-29.
1
[2] M. Bresar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 140 (4) (1988), 1003-1006.
2
[3] M. Bresar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-322.
3
[4] M. Bresar, Characterizations of derivations on some normed algebras with involution, Journal of Algebra. 152 (1992), 454-462.
4
[5] J. Cusack, Jordan derivations on rings, Proc.Amer. Math. Soc. 53 (1975), 1104-1110.
5
[6] H. G. Dales, P. Aiena, J. Eschmeier, K. Laursen and G. A. Willis, Introduction to Banach Algebras, Operators and Harmonic Analysis. Cambridge University Press, 2003.
6
[7] I. N. Herstein, Jordan derivations of prime rings, Proc.Amer. Math. Soc. 8 (1957), 1104-1110.
7
[8] A. Hosseini, A characterization of weak nm-Jordan (; )-derivations by generalized centralizers, Rend. Circ. Mat. Palermo. 64 (2015), 221-227.
8
[9] M. Mirzavaziri and E. Omidvar Tehrani, -double derivations on C-algebras, Bull. Iranian .Math .Soc. 35 (2009), 147-154.
9
[10] J. Vukman, On left Jordan derivations of rings and Banach algebras, Aequ. Math. 75 (2008), 260-266.
10
[11] J. Vukman, A note on generalized derivations of semiprime rings, Taiwanese Journal of Mathematics. 11 (2) (2007), 367-370.
11
[12] J. Vukman and I. Kosi-Ulbl, On derivations in rings with involution, Int. Math. J. 6 (2005), 81-91.
12
[13] J. Vukman and I. Kosi-Ulbl, On some equations related to derivations in rings, Int. J. Math. Math. Sci. 17 (2005), 2703-2710.
13
ORIGINAL_ARTICLE
Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue
Given four complex matrices $A$, $B$, $C$ and $D$ where $A\in\mathbb{C}^{n\times n}$ and $D\in\mathbb{C}^{m\times m}$ and let the matrix $\left(\begin{array}{cc} A & B \ C & D \end{array} \right)$ be a normal matrix and assume that $\lambda$ is a given complex number that is not eigenvalue of matrix $A$. We present a method to calculate the distance norm (with respect to 2-norm) from $D$ to the set of matrices $X \in C^{m \times m}$ such that, $\lambda$ be a multiple eigenvalue of matrix $\left(\begin{array}{cc} A & B \ C & X \end{array} \right)$. We also find the nearest matrix $X$ to the matrix $D$.
http://jlta.iauctb.ac.ir/article_530216_a502b7f8619b310d41d7a1432359e88d.pdf
2017-06-01T11:23:20
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11
28
Normal matrix
multiple eigenvalues
singular value
distance matrices
A.
Nazari
a-nazari@araku.ac.ir
true
1
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
LEAD_AUTHOR
A.
Nezami
true
2
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
AUTHOR
[1] Juan-Miguel Gracia, Francisco E. Velasco, Nearesrt Southeast Submatrix that makes multiple a prescribed eigenvalue. Part 1, Linear Algebra Appl. 430 (2009) 1196-1215.
1
[2] Kh.D. Ikramov, A.M. Nazari, Computational aspects of the use of Malyshev's formula, Zh. Vychisl. Mat. Mat. Fiz. 44 (1) (2004), 3-7.
2
[3] Ross A. Lippert, Fixing two eigenvalues by a minimal perturbation, Linear Algebra Appl. 406 (2005), 177-200.
3
[4] A.N. Malyshev, A formula for the 2-norm distance from a matrix to the set of matrices with multiple eigenvalues, Numer. Math., 83 (1999), 443-454.
4
[5] A.M. Nazari, D. Rajabi, Computational aspect to the nearest matrix with two prescribed eigenvalues, Linear Algebra Appl. 432 (2010), 1-4.
5
ORIGINAL_ARTICLE
New best proximity point results in G-metric space
Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:K\rightarrow E$ is a continuous mapping, then there exists an element $x$ satisfying the condition $d(x,Tx)=\inf \{d(y,Tx):y\in K\}$, where $d$ is a metric on $E$. Recently, Hussain et al. (Abstract and Applied Analysis, Vol. 2014, Article ID 837943) introduced proximal contractive mappings and established certain best proximity point results for these mappings in $G$-metric spaces. The aim of this paper is to introduce certain new classes of auxiliary functions and proximal contraction mappings and establish best proximity point theorems for such kind of mappings in $G$-metric spaces. As consequences of these results, we deduce certain new best proximity and fixed point results in $G$-metric spaces. Moreover, we present certain examples to illustrate the usability of the obtained results.
http://jlta.iauctb.ac.ir/article_530221_121e115915de0dbaa0e435e6c44729b0.pdf
2017-06-01T11:23:20
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73
89
Best proximity point
Generalized proximal weakly G-contraction
G-metric space
A. H.
Ansari
analsisamirmath2@gmail.com
true
1
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
AUTHOR
A.
Razani
razani@sci.ikiu.ac.ir
true
2
Department of Mathematics, Faculty of Science, Imam Khomeini
International University, postal code: 34149-16818, Qazvin, Iran
Department of Mathematics, Faculty of Science, Imam Khomeini
International University, postal code: 34149-16818, Qazvin, Iran
Department of Mathematics, Faculty of Science, Imam Khomeini
International University, postal code: 34149-16818, Qazvin, Iran
LEAD_AUTHOR
N.
Hussain
nhusain@kau.edu.sa
true
3
Department of Mathematics, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia
Department of Mathematics, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia
AUTHOR
[1] A. Amini-Harandi, N. Hussain, F. Akbar, Best proximity point results for generalized contractions in metric spaces, Fixed Point Theory and Applications 2013: 164 (2013).
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[2] M. Asadi, E. Karapinar, P. Salimi, A new approach to G-metric and related fixed point theorems, Journal of Inequalities and Applications, 2013: 454 (2013).
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[3] H. Aydi, E. Karapinar, P. Salimi, Some fixed point results in GP-metric spaces, J. Appl. Math. Article ID 891713 (2012).
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[4] B. S. Choudhury, P. Maity, Best proximity point results in generalized metric spaces, Vietnam J. Mathematics, 10.1007/s10013-015-0141-3.
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[5] C. Di Bari, T. Suzuki, C. Vetro, Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Analysis 69 (11) (2008), 3790-3794.
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[6] K. Fan, Extensions of two fixed point theorems of F.E. Browder, Mathematische Zeitschrift 112 (3) (1969), 234-240.
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[7] N. Hussain, E. Karapinar, P. Salimi, P. Vetro, Fixed point results for Gm-Meir-Keeler contractive and G- (α, ψ)-Meir-Keeler contractive mappings, Fixed Point Theory and Applications 2013: 34 (2013).
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[8] N. Hussain, M. A. Kutbi and P. Salimi, Best proximity point results for modified α-ψ-proximal rational contractions, Abstract and Applied Analysis Article ID 927457 (2013), 14 pages.
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[9] N. Hussain, A. Latif, P. Salimi, Best proximity point results in G-metric spaces, Abstract and Applied Analysis Article ID 837943 (2014), 8 pages.
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[10] N. Hussain, A Latif and P. Salimi, Best proximity point results for modified Suzuki α-ψ-proximal contractions, Fixed Point Theory and Applications 2014: 10 (2014).
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[11] M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl. 2012: 210 (2012).
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[12] F. Moradlou, P. Salimi, P.Vetro, Some new extensions of Edelstein-Suzuki-type fixed point theorem to Gmetric and G-cone metric spaces, Acta Mathematica Scientia 33B (4) (2013), 1049-1058.
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[13] Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297.
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[14] Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl. Article ID 917175 (2009), 10 pages.
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[15] Z. Mustafa, V. Parvaneh, M. Abbas and J.R. Roshan, Some coincidence point results for generalized (ψ, ϕ)- weakly contractive mappings in ordered G-metric spaces, Fixed Point Theory and Applications 2013: 326 (2013).
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[16] Z. Mustafa, A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. Thesis, The University of Newcastle, Australia, 2005.
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[17] S. Radenovi´c, P. Salimi, S. Panteli´c, J. Vujakovi´c, A note on some tripled coincidence point results in G-metric spaces. Int. J. Math. Sci. Eng. Appl. 6 (2012), 23-38.
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[18] A. Razani, V. Parvaneh, On generalized weakly G-contractive mappings in partially ordered G-metric spaces, Abstr. Appl. Anal. Article ID 701910 (2012), 18 pages.
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[19] S. Sadiq Basha, Extensions of Banach’s contraction principle. Numer. Funct. Anal. Optim. 31 (2010), 569-576.
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[20] P. Salimi, P. Vetro, A result of suzuki type in partial G-metric spaces, Acta Mathematica Scientia 34B (2) (2014), 1-11.
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[21] B. Samet, C. Vetro, F. Vetro, Remarks on G-metric spaces, Int. J. Anal. Article ID 917158 (2013), 6 pages.
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[22] T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal. Theory, Methods Applications, 71 (7-8) (2009), 2918-2926.
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