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 $K.$
| Published in: | Applied General Topology |
|---|---|
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2017-10-01
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| Subjects: | |
| Online Access: | https://polipapers.upv.es/index.php/AGT/article/view/7452 |