Fixed points for uniformly asymptotically Hölder-Lipschitz mappings
Abstract
In this work, we show that if K is a nonempty, closed, bounded, and convex subset of X and 1≤ γ<√(N(X)), where N(X) denotes the Bynum normal structure coefficient, then every uniformly asymptotically Hölder γ-Lipschitz mapping T: K→ K has a fixed point. To achieve this, it was necessary to guarantee the existence of a subsequence of a bounded sequence whose asymptotic diameter is controlled by the quantity D({xn}), introduced by Jiménez-Melado, while simultaneously preserving the asymptotic radii at every point of the closure of the linear span generated by the original sequence. This allowed us to remove the Hölder exponent from the calculations and obtain a Hölder-type extension of the Casini--Maluta, Lim--Xu, and, consequently, Kim--Xu theorems.
Related
- Fixed point results for mappings of asymptotically Hölder nonexpansive type
- Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
- Transversal Hölder Criteria and Dini--Zygmund Endpoint Regularity for Hyperbolic Harmonic Mappings
- Uniformly Lipschitz Hyperbolic Group Actions on ℓp
- The Kadets--Werner modification of Bourgain--Rosenthal space is asymptotically midpoint uniformly convex
BibTeX
@misc{josino2026fixed,
title = {{Fixed points for uniformly asymptotically Hölder-Lipschitz mappings}},
author = {Luciano G. Josino and Carlos Sérgio R. da Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14327},
eprint = {2610.14327},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14327},
}
RIS
TY - UNPB
TI - Fixed points for uniformly asymptotically Hölder-Lipschitz mappings
AU - Luciano G. Josino
AU - Carlos Sérgio R. da Silva
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14327
UR - https://arxiv.org/abs/2610.14327
AB - In this work, we show that if K is a nonempty, closed, bounded, and convex subset of X and 1≤ γ<√(N(X)), where N(X) denotes the Bynum normal structure coefficient, then every uniformly asymptotically Hölder γ-Lipschitz mapping T: K→ K has a fixed point. To achieve this, it was necessary to guarantee the existence of a subsequence of a bounded sequence whose asymptotic diameter is controlled by the quantity D({x_n}), introduced by Jiménez-Melado, while simultaneously preserving the asymptotic radii at every point of the closure of the linear span generated by the original sequence. This allowed us to remove the Hölder exponent from the calculations and obtain a Hölder-type extension of the Casini--Maluta, Lim--Xu, and, consequently, Kim--Xu theorems.
ER -