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<p>In this work we introduced a class of Banach spaces more general than the class of uniformly nonsquare spaces, called <i>H</i>-convex spaces. We show that <i>H</i>-convex Banach spaces are superreflexive and that a wide class of them implies the fixed point property for nonexpansive mappings. We also study the relationship between <i>H</i>-convexity and some classical geometric properties of Banach spaces.</p>

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A Generalization of Uniform Nonsquareness Given by the Hausdorff Distance

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Chayan Adelki De La Cruz-Reyes,
  • Omar Muñiz-Pérez

摘要

In this work we introduced a class of Banach spaces more general than the class of uniformly nonsquare spaces, called H-convex spaces. We show that H-convex Banach spaces are superreflexive and that a wide class of them implies the fixed point property for nonexpansive mappings. We also study the relationship between H-convexity and some classical geometric properties of Banach spaces.