Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
Normalized laplacian spectrum of two new types of join graphs
1
9
EN
M.
Hakimi-Nezhaad
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
m.hakimi20@gmail.com
M.
Ghorbani
Department of Mathematics, Faculty of Science, Shahid Rajaee
Teacher Training University, Tehran, 16785-136, Iran
mghorbani@sru.ac.ir
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.
Join of graphs,normalized Laplacian eigenvalue,integral eigenvalue
http://jlta.iauctb.ac.ir/article_530214.html
http://jlta.iauctb.ac.ir/article_530214_f255c8fba799a482b12f622798cb0e72.pdf
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
The method of radial basis functions for the solution of nonlinear Fredholm integral equations system.
11
28
EN
J.
Nazari
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
jinoosnazari@yahoo.com
M.
Nili Ahmadabadi
Department of Mathematics, Najafabad Branch, Islamic Azad University,
Najafabad, Iran
mneely59@hotmail.com
H.
Almasieh
Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University,
Isfahan, Iran
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.
Radial basis functions,Fredholm integral equations system
http://jlta.iauctb.ac.ir/article_530220.html
http://jlta.iauctb.ac.ir/article_530220_b5806589bc793ef8a1c29b7f681518e6.pdf
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
Unique common coupled fixed point theorem for four maps in $S_b$-metric spaces
29
43
EN
K. P. R.
Rao
Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar,
Guntur-522 510, Andhra Pradesh, India
kprrao2004@yahoo.com
G. V. N.
Kishore
Department of Mathematics, K L University, Vaddeswaram, Guntur-522 502,
Andhra Pradesh, India
kishore.apr2@gmail.com
Sk.
Sadik
Department of Mathematics, Sir C R R College of Engineering, Eluru,
West Godavari-534 007, Andhra Pradesh, India
sadikcrrce@gmail.com
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.
$S_b$-metric space,$w$-compatible pairs,$S_b$-completeness,coupled fixed point
http://jlta.iauctb.ac.ir/article_530217.html
http://jlta.iauctb.ac.ir/article_530217_54695cc3c57d07c6a55288deb5e2347a.pdf
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
Coupled fixed point theorems involving contractive condition of integral type in generalized metric spaces
45
53
EN
R.
Shah
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
safeer_rahim@yahoo.com
A.
Zada
Department of Mathematics, University of Peshawar, Peshawar, Pakistan
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.
Generalized metric space,coupled fixed points,integral type contractive mapping,fixed point
http://jlta.iauctb.ac.ir/article_530218.html
http://jlta.iauctb.ac.ir/article_530218_759caf33a4b08455a2a95e5a421a0c49.pdf
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
Characterization of $delta$-double derivations on rings and algebras
55
65
EN
A.
Hosseini
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran
hosseini.amin82@gmail.com
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 $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Sigma^{n-2}_{k=0} Sigma^{n-2-k}_{i=0} x^kdelta(x)x^idelta(x)x^{n-2-k-i}$$ is fulfilled for all $xin mathcal{R}$. If $delta(1) = 0$, then $d$ is a Jordan $delta$-double derivation. In particular, if $mathcal{R}$ is a semiprime algebra and further, $delta^2(x^2) = delta^2(x)x + xdelta^2(x) + 2(delta(x))^2$ holds for all $xin mathcal{R}$, then $d-frac{1}{2}delta^2$ is an ordinary derivation on $mathcal{R}$.
$delta$-Double derivation,Jordan $delta$-double derivation,$n$-torsion free semiprime ring
http://jlta.iauctb.ac.ir/article_530219.html
http://jlta.iauctb.ac.ir/article_530219_060ffd6f8fdb6be2b26f37f261c10c73.pdf
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue
67
72
EN
A.
Nazari
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
a-nazari@araku.ac.ir
A.
Nezami
Department of Mathematics, Arak University,
P.O. Box 38156-8-8349, Arak, Iran
Given four complex matrices $A$, $B$, $C$ and $D$ where $Ainmathbb{C}^{ntimes n}$ and $Dinmathbb{C}^{mtimes m}$ 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 $D$.
Normal matrix,multiple eigenvalues,singular value,distance matrices
http://jlta.iauctb.ac.ir/article_530216.html
http://jlta.iauctb.ac.ir/article_530216_cbb677d2395447e0a7770ad0672a7b3b.pdf
Central Tehran Branch. IAU
Journal of Linear and Topological Algebra (JLTA)
2252-0201
2345-5934
06
01
2017
03
01
New best proximity point results in G-metric space
73
89
EN
A. H.
Ansari
Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
analsisamirmath2@gmail.com
A.
Razani
Department of Mathematics, Faculty of Science, Imam Khomeini
International University, postal code: 34149-16818, Qazvin, Iran
razani@sci.ikiu.ac.ir
N.
Hussain
Department of Mathematics, King Abdulaziz University,
P.O. Box 80203, Jeddah 21589, Saudi Arabia
nhusain@kau.edu.sa
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 $T:Krightarrow E$ is a continuous mapping, then there exists an element $x$ satisfying the condition $d(x,Tx)=inf {d(y,Tx):yin K}$, 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.
Best Proximity Point,Generalized proximal weakly G-contraction,G-metric space
http://jlta.iauctb.ac.ir/article_530221.html
http://jlta.iauctb.ac.ir/article_530221_9fd2d17d3a16fbabe8642315db047b3a.pdf