Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201On some open problems in cone metric space over Banach algebra261267536118ENA. AhmedDepartment of Humanities and Basics Sciences, School of Engineering, Matoshri Pratishthan Group of Institutions, Nanded, India0000-0001-7313-5991Z. D. MitrovicUniversity of Banja Luka, Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and HerzegovinaJ. N. SalunkeSchool of Mathematical Sciences, Swami Ramanandh Teerth Marathwada University, Nanded, IndiaJournal Article20171024In 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].http://jlta.iauctb.ac.ir/article_536118_fb4cb5258f2239d175a2738adf45e36f.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201A fixed point method for proving the stability of ring $(alpha, beta, gamma)$-derivations in $2$-Banach algebras269276536116ENM. Eshaghi GordjiDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranS. AbbaszadehDepartment of Mathematics, Payame Noor University, P.O. BOX 19395-4697, Tehran, Iran0000-0002-8257-0116Journal Article20171003In 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.http://jlta.iauctb.ac.ir/article_536116_a2fa96c0595bab5c5faf576f3e547c7f.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201A solution of nonlinear fractional random differential equation via random ﬁxed point technique277287536117ENR. A. RashwanDepartment of Mathematics, Faculty of Science, Assuit University, Assuit 71516, EgyptH. A. HammadDepartment of Mathematics, Faculty of Science, Sohag University, Sohag 82524, EgyptJournal Article20171001In 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.http://jlta.iauctb.ac.ir/article_536117_32277bf22266c36e920243012bcbba9a.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201Common best proximity points for $(psi-phi)$-generalized weak proximal contraction type mappings289300536813ENK. K. M. SarmaDepartment of Mathematics, Andhra University, IndiaG. YohannesDepartment of Mathematics, Wolkite University, EthiopiaJournal Article20171030In 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.http://jlta.iauctb.ac.ir/article_536813_653e4442ecbacac4ce633827f7ee61f5.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201Coincidence points and common fixed points for hybrid pair of mappings in b-metric spaces endowed with a graph301321536814ENS. K. MohantaDepartment of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, IndiaS. PatraDepartment of Mathematics, West Bengal State University, Barasat, 24 Parganas (North), Kolkata-700126, West Bengal, IndiaJournal Article20171030In 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.http://jlta.iauctb.ac.ir/article_536814_ff3f0b6e868b991637ce324bf9e5d15f.pdfCentral Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201060420171201Fixed points of weak $psi$-quasi contractions in generalized metric spaces323329537759ENK. P. R. Sastry8-28-8/1, Tamil Street, China Waltair, Visakhapatnam-530 017, IndiaG. V. R. BabuDepartment of Mathematics, Andhra University, Visakhapatnam-530 003, IndiaP. S. KumarDepartment of Mathematics, Andhra University, Visakhapatnam-530 003, IndiaJournal Article20171029In 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.http://jlta.iauctb.ac.ir/article_537759_95df6849b60c60f26dbd2462fbe1c516.pdf