Hölder-contractive mappings, nonlinear extension problem and fixed point free results
نویسندگان
چکیده
For a bounded closed convex set K, in this note, we study the FPP for α-Hölder nonexpansive maps, i.e. mappings T:K→K which ‖Tx−Ty‖≤‖x−y‖α all x,y∈K, α∈(0,1). First, note that only finite-dimensional spaces have Hölder-FPP. Moreover, unit ball BX of any infinite-dimensional space fails Hölder maps with d(T,BX)>0, where d(T,K) denotes minimal displacement T. We further show reflexivity and weak sequential continuity are sufficient conditions to capture fixed points Hölder-Lipschitz orbits. Next focus on existence point free d(T,K)≤φ(α) either φ(α)=0 or φ(α)→0 as α→1. Interesting results obtained c, c0 ℓ1, also Lp-spaces p∈{1,∞}. problem containing copies ℓ1. Some questions left open.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2023
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2023.127521