Several Geometric Properties in Banach Spaces and Their Further Application in Orlicz Spaces

Xiaoxia Wang; Yunan Cui; Yaoming Niu

doi:10.3390/axioms14120928

,

and

¹

School of Mathematics and Computer Engineering, Ordos Institute of Technology, Ordos 017000, China

²

Faculty of Mathematic, Harbin Cambridge University, Harbin 150069, China

^*

Author to whom correspondence should be addressed.

Axioms2025, 14(12), 928;https://doi.org/10.3390/axioms14120928

This article belongs to the Special Issue Advances in Functional Analysis and Banach Space

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Abstract

In this paper, locally nearly uniformly convex (LNUC) is studied in Banach space. Furthermore, the implication relationship between (LNUC) and the Kadec–Klee property (KK), the fixed–point property (FPP) are investigated in Banach space. Finally, the relationship between the uniform Kadec−Klee property (UKK), the coordinate-wise uniform Kadec–Klee property (UKK_C) , the coordinate-wise Kadec–Klee property (H_c) and δ₂ conditions are investigated in Orlicz sequence spaces equipped with the Orlicz norm, meanwhile we get a criteria that Orlicz sequence spaces equipped with the Orlicz norm are (LNUC).

Keywords:

locally nearly uniformly convex; Kadec–Klee property; uniform Kadec−Klee; fixed–point property; Orlicz sequence spaces

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