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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… Click to show full abstract
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 $K.$
Keywords:
theorems non;
point;
non convex;
point theorems;
convex sets;
fixed point
Journal Title: Applied general topology
Year Published: 2017
Link to full text (if available)
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Journal Title: Applied general topology
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!