@article{Marrero2025, 
author = {Isabel Marrero},
title = {Brøndsted's fixed point theorem in LUR spaces},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {9},
pages = {20932-20946},
keywords = {Brøndsted fixed point theorem, directional operator, locally uniformly rotund space, Orlicz space, renorming, uniformly rotund space},
url = {https://www.sciopen.com/article/10.3934/math.2025935},
doi = {10.3934/math.2025935},
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.}
}