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arXiv · 1209.5368

On the Suzuki nonexpansive-type mappings

Anna Betiuk-Pilarska·Andrzej Wiśnicki
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Abstract

It is shown that if $C$ is a nonempty convex and weakly compact subset of a Banach space $X$ with $M(X)>1$ and $T:C\rightarrow C$ satisfies condition $(C)$ or is continuous and satisfies condition $(C_{\lambda})$ for some $\lambda \in (0,1)$, then $T$ has a fixed point. In particular, our theorem holds for uniformly nonsquare Banach spaces. A similar statement is proved for nearly uniformly noncreasy spaces.

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Anna Betiuk-Pilarska, Andrzej Wiśnicki. 2012-09-24. On the Suzuki nonexpansive-type mappings. https://arxiv.org/abs/1209.5368

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