Some generalizations of common fixed point problems with applications

Some Generalizations of Caristi’s Fixed Point Theorem with Applications

In this paper, we prove some generalizations of Caristi’s fixed point theorem, and then we give applications to Ekeland’s variational principle and maximal element theorem. Mathematics Subject Classification: 47H10, 54H25

Simultaneous generalizations of known fixed point theorems for a Meir-Keeler type condition with applications

In this paper, we first establish a new fixed point theorem for a Meir-Keeler type condition. As an application, we derive a simultaneous generalization of Banach contraction principle, Kannan's fixed point theorem, Chatterjea's fixed point theorem and other fixed point theorems. Some new fixed point theorems are also obtained.

New Best Proximity Point Theorems with Applications to Simultaneous Generalizations of Common Fixed Point Theorems

In this work, we first introduce the concept of approximate sequence and establish some new convergence theorems for approximate sequences. By applying our new convergence theorems, we obtain new best proximity point theorems which improve and generalize some known results in the literature. As applications, some simultaneous generalizations of common fixed point theorems of Banach type, Kannan...

Some Generalizations of Jungck's Fixed Point Theorem

Some Generalizations of Mulit-Valued Version of Schauder’s Fixed Point Theorem with Applications

In this article, a generalization of a Kakutani-Fan fixed point theorem for multi-valued mappings in Banach spaces is proved under weaker upper semi-continuity condition and it is further applied to derive a generalized version of Krasnoselskii’s fixed point theorem and some nonlinear alternatives of Leray-Schauder type for multi-valued closed mappings in Banach spaces. RESUMEN En este artículo...