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

Alabbadi, Ismail Abdel Hamid; Jawdat, Jamila

doi:10.28919/jmcs/6460

J. Math. Comput. Sci. 11 (2021), 7476–7486

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

Ismail Abdel Hamid Alabbadi, Jamila Jawdat

PDF (428.4 KB) https://doi.org/10.28919/jmcs/6460

Abstract

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

Published: 28 September 2021
Volume: 11 (2021)
License: CC BY 3.0

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.

Cite this article

I. A. H. Alabbadi, J. Jawdat, Mutual proximinality of two sets in Lp(µ, X), J. Math. Comput. Sci. 11 (2021), 7476–7486. https://doi.org/10.28919/jmcs/6460

BibTeX

@article{Alabbadi2021,
  author  = {Alabbadi, Ismail Abdel Hamid and Jawdat, Jamila},
  title   = {Mutual proximinality of two sets in Lp(µ, X)},
  journal = {J. Math. Comput. Sci.},
  volume  = {11},
  year    = {2021},
  pages   = {7476--7486},
  doi     = {10.28919/jmcs/6460}
}