Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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EXPANSION THEORY FOR THE TWO-SIDED BEST SIMULTANEOUS APPROXIMATIONS

  • RHEE, HYANG JOO (Department of Mathematics, College of Natural Sciences, Duksung Women's University)
  • Received : 2021.04.09
  • Accepted : 2021.04.22
  • Published : 2021.05.30
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Abstract

In this paper, we study the characterizations of two-sided best simultaneous approximations for ℓ-tuple subset from a closed convex subset of ℝm with ℓm1(w)-norm. Main fact is, k* is a two-sided best simultaneous approximation to F from K if and only if there exist f1, …, fp in F, for any k ∈ K $${\mid}{\sum\limits_{i=1}^{m}}sgn(f_{ji}-k^*_i)k_iw_i{\mid}{\leq}\;{\sum\limits_{i{\in}Z(f_j-k^*)}}\;{\mid}k_i{\mid}w_i$$ for each j = 1, …, p and 𝐰 ∈ W.

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References

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