DOI: 10.24193/fpt-ro.2023.2.07

Authors: T. Domínguez Benavides and P. Lorenzo Ramírez

Abstract: We prove the existence of fixed points for mappings which satisfy some asymptotic nonexpansive conditions in Banach spaces which are either nearly uniformly convex or they satisfy that asymptotic centers of bounded sequences are compact. Nominally, we consider pointwise eventually nonexpansive mappings, pointwise asymptotically nonexpansive mappings and asymptotically type nonexpansive mappings. We do not assume the existence of a continuous iterate, solving some long-standing open questions about existence of a fixed point for these mappings in absence of continuity [7]

Key Words and Phrases: Fixed point, pointwise nonexpansive mapping, nearly uniform convexity, asymptotic radius.

2010 Mathematics Subject Classification: 47H09, 47H10.

Published on-line: June 15th, 2023.

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