Some fixed point theorems on non-convex sets

In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$

Bibliographic Details
Published in:Applied General Topology
Main Authors: Mohanasundaram Radhakrishnan, S. Rajesh, Sushama Agrawal
Format: Article
Language:English
Published: Universitat Politècnica de València 2017-10-01
Subjects:
fixed points
nonexpansive mappings
$T-$regular set
$k-$uniform convex Banach spaces
Opial property.
Online Access:https://polipapers.upv.es/index.php/AGT/article/view/7452

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