"A note in approximative compactness and midpoint locally k-uniform rotundity in Banach spaces"

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Abstract In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is… Click to show full abstract

Abstract In this article, we prove the following results: (1) A Banach space X is weak midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively weakly compact k-Chebyshev set; (2) A Banach space X is midpoint locally k-uniformly rotund if and only if every closed ball of X is an approximatively compact k-Chebyshev set.

Keywords: note approximative; approximative compactness; compactness midpoint; midpoint; banach; midpoint locally

Journal Title: Acta Mathematica Scientia
Year Published: 2018

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