Mutual proximinality of two sets in Lp(µ, X)

Ismail Abdel Hamid Alabbadi, Jamila Jawdat

Abstract


In this paper, we study mutual best approximation of two sets in the p–Bochner function spaces Lp(µ,X),  1 ≤ p < ∞. We give some sufficient conditions on M and K as subsets of the Banach space X to guarantee that Lp(and Lp( are mutually proximinal subsets in Lp(µ,X). The main issue in this work is that we state and prove a distance formula for mutual best approximation between the two sets Lp(and Lp( in Lp(µ,X), for  1 ≤ p < ∞. Then we use this formula to obtain some other results related to our study.

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Published: 2021-09-28

How to Cite this Article:

Ismail Abdel Hamid Alabbadi, Jamila Jawdat, Mutual proximinality of two sets in Lp(µ, X), J. Math. Comput. Sci., 11 (2021), 7476-7486

Copyright © 2021 Ismail Abdel Hamid Alabbadi, Jamila Jawdat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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