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Research Article | Open Access

On minimal asymptotically nonexpansive mappings

Juan Rafael Acosta-Portilla1( ), Lizbeth Yolanda Garrido-Ramírez2
Instituto de Investigaciones y Estudios Superiores Económicos y Sociales, Universidad Veracruzana, México
Facultad de Economía, Universidad Veracruzana, México
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Abstract

In this paper we present the following two results: 1.- A characterization of the renorming invariant family of asymptotically nonexpansive mappings defined on a convex, closed and bounded set of a Banach space; 2.- A comparison of the renorming invariant family of asymptotically nonexpansive mappings with the renorming invariant family of nonexpansive mappings. Additionally, a series of examples are shown for general and particular cases.

Keywords

renormingasymptotically nonexpansive mappinglipschitzian mappingnonexpansive mapping
CLC number: 46B03, 46B20, 47H09

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AIMS Mathematics
Volume 8 Issue 4,
April 2023
Pages 9416-9435
DOI: 10.3934/math.2023474

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Cite this article:
Acosta-Portilla JR, Garrido-Ramírez LY. On minimal asymptotically nonexpansive mappings. AIMS Mathematics, 2023, 8(4): 9416-9435. https://doi.org/10.3934/math.2023474

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Received: 01 December 2022
Revised: 08 February 2023
Accepted: 09 February 2023
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)