Special Issue on Fixed Point Theory Fixed point theory
1. On some open problems in cone metric space over Banach algebra

A. Ahmed; Z. D. Mitrovic; J. N. Salunke

Volume 06, Issue 04 , Autumn 2017, Pages 261-267

Abstract
  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, ...  Read More

Special Issue on Fixed Point Theory Fixed point theory
2. A fixed point method for proving the stability of ring $(\alpha, \beta, \gamma)$-derivations in $2$-Banach algebras

M. Eshaghi Gordji; S. Abbaszadeh

Volume 06, Issue 04 , Autumn 2017, Pages 269-276

Abstract
  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.  Read More

Special Issue on Fixed Point Theory Fixed point theory
3. A solution of nonlinear fractional random differential equation via random fixed point technique

R. A. Rashwan; H. A. Hammad

Volume 06, Issue 04 , Autumn 2017, Pages 277-287

Abstract
  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.  Read More

Special Issue on Fixed Point Theory Fixed point theory
4. Common best proximity points for $(\psi-\phi)$-generalized weak proximal contraction type mappings

K. K. M. Sarma; G. Yohannes

Volume 06, Issue 04 , Autumn 2017, Pages 289-300

Abstract
  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.  Read More

Special Issue on Fixed Point Theory Fixed point theory
5. Coincidence points and common fixed points for hybrid pair of mappings in b-metric spaces endowed with a graph

S. K. Mohanta; S. Patra

Volume 06, Issue 04 , Autumn 2017, Pages 301-321

Abstract
  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 ...  Read More

Special Issue on Fixed Point Theory Fixed point theory
6. Fixed points of weak $\psi$-quasi contractions in generalized metric spaces

K. P. R. Sastry; G. V. R. Babu; P. S. Kumar

Volume 06, Issue 04 , Autumn 2017, Pages 323-329

Abstract
  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 ...  Read More