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

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  • Suyalatu Wulede

    (Inner Mongolia Normal University)

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.

Suggested Citation

  • Suyalatu Wulede, 2021. "The locally k-uniformly extremely convex and midpoint locally k-uniformly extremely convex Banach spaces," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(2), pages 512-520, June.
    • Handle: RePEc:spr:indpam:v:52:y:2021:i:2:d:10.1007_s13226-021-00053-4
    DOI: 10.1007/s13226-021-00053-4
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