{"paper":{"title":"Fixed point results for asymptotically H\\\"older nonexpansive type mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Carlos S\\'ergio R. da Silva, Cleon S. Barroso","submitted_at":"2026-05-29T00:16:18Z","abstract_excerpt":"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 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30678","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30678/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}