On some open problems in cone metric space over Banach algebra
A.
Ahmed
Department of Humanities and Basics Sciences, School of Engineering, Matoshri Pratishthan Group of Institutions, Nanded, India
author
Z. D.
Mitrovic
University of Banja Luka, Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina
author
J. N.
Salunke
School of Mathematical Sciences, Swami Ramanandh Teerth Marathwada University, Nanded, India
author
text
article
2017
eng
In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. and Engg. Appl. (6) (2012), 129-136].
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
06
v.
04
no.
2017
261
267
http://jlta.iauctb.ac.ir/article_536118_fb4cb5258f2239d175a2738adf45e36f.pdf
A fixed point method for proving the stability of ring $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras
M.
Eshaghi Gordji
Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
author
S.
Abbaszadeh
Department of Mathematics, Payame Noor University, P.O. BOX 19395-4697, Tehran, Iran
author
text
article
2017
eng
In this paper, we first present the new concept of $2$-normed algebra. We investigate the structure of this algebra and give some examples. Then we apply a fixed point theorem to prove the stability and hyperstability of $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
06
v.
04
no.
2017
269
276
http://jlta.iauctb.ac.ir/article_536116_a2fa96c0595bab5c5faf576f3e547c7f.pdf
A solution of nonlinear fractional random differential equation via random ﬁxed point technique
R. A.
Rashwan
Department of Mathematics, Faculty of Science, Assuit University, Assuit 71516, Egypt
author
H. A.
Hammad
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
author
text
article
2017
eng
In this paper, we investigate a new type of random $F$-contraction and obtain a common random fixed point theorem for a pair of self stochastic mappings in a separable Banach space. The existence of a unique solution for nonlinear fractional random differential equation is proved under suitable conditions.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
06
v.
04
no.
2017
277
287
http://jlta.iauctb.ac.ir/article_536117_32277bf22266c36e920243012bcbba9a.pdf
Common best proximity points for $(\psi-\phi)$-generalized weak proximal contraction type mappings
K. K. M.
Sarma
Department of Mathematics, Andhra University, India
author
G.
Yohannes
Department of Mathematics, Wolkite University, Ethiopia
author
text
article
2017
eng
In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
06
v.
04
no.
2017
289
300
http://jlta.iauctb.ac.ir/article_536813_653e4442ecbacac4ce633827f7ee61f5.pdf
Coincidence points and common fixed points for hybrid pair of mappings in b-metric spaces endowed with a graph
S. K.
Mohanta
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India
author
S.
Patra
Department of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, India
author
text
article
2017
eng
In this paper, we introduce the notion of strictly (α,ψ,ξ)-G-contractive mappings in b-metric spaces endowed with a graph G. We establish a sufficient condition for existence and uniqueness of points of coincidence and common fixed points for such mappings. Our results extend and unify many existing results in the literature. Finally, we construct some examples to analyze and support our results.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
06
v.
04
no.
2017
301
321
http://jlta.iauctb.ac.ir/article_536814_ff3f0b6e868b991637ce324bf9e5d15f.pdf
Fixed points of weak $\psi$-quasi contractions in generalized metric spaces
K. P. R.
Sastry
8-28-8/1, Tamil Street, China Waltair, Visakhapatnam-530 017, India
author
G. V. R.
Babu
Department of Mathematics, Andhra University, Visakhapatnam-530 003, India
author
P. S.
Kumar
Department of Mathematics, Andhra University, Visakhapatnam-530 003, India
author
text
article
2017
eng
In this paper, we introduce the notion of weak $\psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.
Journal of Linear and Topological Algebra (JLTA)
Central Tehran Branch, Islamic Azad University
2252-0201
06
v.
04
no.
2017
323
329
http://jlta.iauctb.ac.ir/article_537759_95df6849b60c60f26dbd2462fbe1c516.pdf