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Research Article | Open Access

Brøndsted's fixed point theorem in LUR spaces

Departamento de Análisis Matemático, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
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Abstract

In this paper, we establish novel characterizations of locally uniformly rotund (LUR) Banach spaces. Building on these results, we prove that Zubelevich's relaxed version of Brøndsted's fixed point theorem for uniformly rotund spaces holds in the strictly broader class of LUR spaces. As an illustration, we derive existence results for fixed points of directional operators on Orlicz spaces under conditions where neither Brøndsted's nor Zubelevich's theorems apply.

Keywords

Brøndsted fixed point theoremdirectional operatorlocally uniformly rotund spaceOrlicz spacerenorminguniformly rotund space
CLC number: 47H10, 46B20, 46B40, 46E30

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 20932-20946
DOI: 10.3934/math.2025935

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Cite this article:
Marrero I. Brøndsted's fixed point theorem in LUR spaces. AIMS Mathematics, 2025, 10(9): 20932-20946. https://doi.org/10.3934/math.2025935

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Received: 27 July 2025
Revised: 30 August 2025
Accepted: 08 September 2025
Published: 12 September 2025
©2025 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)