Fixed point results for asymptotically Hölder nonexpansive type mappings
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913172035731456 |
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| author | Barroso, Cleon S. da Silva, Carlos Sérgio R. |
| author_facet | Barroso, Cleon S. da Silva, Carlos Sérgio R. |
| contents | In this work, we extend Goebel-Kirk fixed point theorems to the setting of mappings of asymptotically Hölder-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 Hölder-nonexpansive type and possesses no continuous iterates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30678 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fixed point results for asymptotically Hölder nonexpansive type mappings Barroso, Cleon S. da Silva, Carlos Sérgio R. Functional Analysis In this work, we extend Goebel-Kirk fixed point theorems to the setting of mappings of asymptotically Hölder-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 Hölder-nonexpansive type and possesses no continuous iterates. |
| title | Fixed point results for asymptotically Hölder nonexpansive type mappings |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2605.30678 |