The locally k-uniformly extremely convex and midpoint locally k-uniformly extremely convex Banach spaces

Suyalatu Wulede ()
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Suyalatu Wulede: Inner Mongolia Normal University

Indian Journal of Pure and Applied Mathematics, 2021, vol. 52, issue 2, 512-520

Abstract: Abstract The locally k-uniformly extremely convex Banach spaces are introduced. It is shown here that every locally k-uniformly extremely convex space is locally $$(k+1)$$ ( k + 1 ) -uniformly extremely convex space, but the converse implication is not true. Some properties of locally k-uniformly extremely convex spaces are given. Specially, it is proved that if the second dual of Banach space X is locally 2-uniformly extremely convex, then X is reflexive. In addition, the notion of midpoint locally k-uniformly extreme convexity is introduced and its relations to other type convexity are given.

Keywords: Banach space; Locally k-uniformly extremely convex space; Midpoint locally k-uniformly convex space; 46B09; 46B20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13226-021-00053-4

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