Abstract
In this paper, we introduce the concept of R-nonexpansive self-mappings defined on a suitable subset K of a Banach space, wherein R stands for a transitive binary relation on K, and utilize the same to prove a relation-theoretic variant of classical Browder–Göhde fixed point theorem. As consequences of our newly proved results, we are able to derive several core fixed-point theorems existing in the literature.
Highlights
Metric fixed-point theory is a relatively old but still young area of research which occupies an important place in nonlinear functional analysis
We present the relation-theoretic variants of monotone nonexpansive mappings and order intervals
Main Results For the sake of self-containment, we recall the following well-known results due to Smulian [37], which characterizes the reflexivity of Banach space
Summary
Metric fixed-point theory is a relatively old but still young area of research which occupies an important place in nonlinear functional analysis. Let H be a Hilbert space, K a bounded, closed and convex subset of H and T : K → K a nonexpansive mapping. The class of “uniformly convex Banach spaces" is adjudged suitable to prove fixed-point results for nonexpansive mappings.
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