Brøndsted's fixed point theorem in LUR spaces

Isabel Marrero; Isabel Marrero

doi:10.3934/math.2025935

AIMS Mathematics

2025, Volume 10, Issue 9: 20932-20946. doi: 10.3934/math.2025935

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Brøndsted's fixed point theorem in LUR spaces

Isabel Marrero ^{1,2
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1.
Departamento de Análisis Matemático, Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain
2.
Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna (ULL), 38200 La Laguna, Tenerife, Spain

Received: 27 July 2025 Revised: 30 August 2025 Accepted: 08 September 2025 Published: 12 September 2025
MSC : 47H10, 46B20, 46B40, 46E30

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.
- Brøndsted fixed point theorem,
- directional operator,
- locally uniformly rotund space,
- Orlicz space,
- renorming,
- uniformly rotund space
Citation: Isabel Marrero. Brøndsted's fixed point theorem in LUR spaces[J]. AIMS Mathematics, 2025, 10(9): 20932-20946. doi: 10.3934/math.2025935

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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.

References

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