Convergence of iterates of nonexpansive mappings and orbits of nonexpansive semigroups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:475

Article

Grzesik, Aleksandra¹  Kaczor, Wieslawa²  Kuczumow, Tadeusz²  Reich, Simeon³ 

[1] Rzeszow Tech Univ, Wydzial Matemat & Fizyki Stosowanej, PL-35959 Rzeszow, Poland

[2] UMCS, Inst Matemat, PL-20031 Lublin, Poland

[3] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel

关键词: Fixed point;    Iterates;    Locally uniformly rotund set;    Nonexpansive mapping;    Semigroup of nonexpansive mappings;    Uniform convexity;   

DOI  :  10.1016/j.jmaa.2019.02.053

来源: Elsevier

【 摘 要 】

Let (X, parallel to.parallel to) be a uniformly convex Banach space and let C be a bounded closed and convex subset of X. Assume that C has nonempty interior and is locally uniformly rotund. Let T be a nonexpansive self-mapping of C. If T has no fixed point in the interior of C, then there exists a unique point (x) over tilde on the boundary of C such that each sequence of iterates of T converges in norm to (x) over tilde. We also establish an analogous result for nonexpansive semigroups. (C) 2019 Published by Elsevier Inc.

【 授权许可】

Free