The aim of this paper is to prove some best proximity point theorems for new classes of cyclic mappings, called pointwise cyclic orbital contractions and asymptotic pointwise cyclic orbital contractions. We also prove a convergence theorem of best proximity point for relatively nonexpansive mappings in uniformly convex Banach spaces.
In this article, we prove a fixed point theorem for cyclic relatively nonexpansive mappings in the setting of generalized semimetric spaces by using a geometric notion of seminormal structure and then we conclude some results in uniformly convex Banach spaces. We also discuss on the stability of seminormal structure in generalized semimetric spaces.
Relatively nonexpansive mappings and equilibrium problems are considered based on a shrinking projection method. Using properties of the generalizedf-projection operator, a strong convergence theorem for relatively nonexpansive mappings and equilibrium problems is proved in Banach spaces under some suitable conditions.
Abstract
In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$
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A
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spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.
Existence and Convergence Theorems of Best Proximity Points
