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arXiv · 2605.30678

Fixed point results for asymptotically H\"older nonexpansive type mappings

Cleon S. Barroso·Carlos Sérgio R. da Silva
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Abstract

In this work, we extend Goebel-Kirk fixed point theorems to the setting of mappings of asymptotically H\"older-nonexpansive type. By providing several non-trivial examples, we show that this new framework strictly contains its classical counterparts. Furthermore, we prove that if a Banach space contains an isomorphic copy of either $c_0$ or $\ell_1$, then the fixed point property (FPP) for this class of mappings fails. Finally, we show that every infinite-dimensional Banach space contains a compact convex set $K$ admitting a fixed-point free, affine self-mapping $T$ which is of asymptotically H\"older-nonexpansive type and possesses no continuous iterates.

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Cleon S. Barroso, Carlos Sérgio R. da Silva. 2026-05-29. Fixed point results for asymptotically H\"older nonexpansive type mappings. https://arxiv.org/abs/2605.30678

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