Equivalence relations on approximation theory

Document Type : Research Paper


Faculty of Mathematics, Yazd University, Yazd, Iran


In this paper, we define relations between the best approximation and the worst approximation. We show that these relations are equivalence relations if the sets are Chebyshev or uniquely remotal. We obtain cosets sets of best approximation and cosets sets of worst approximation. We obtain some results on these sets, for example, compactness and weakly compactness. Finally, we consider the semi-inner products (Lumer-Giles) and semi-inner(usual).


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Volume 14, Issue 4
April 2023
Pages 313-322
  • Receive Date: 08 August 2021
  • Accept Date: 16 December 2021
  • First Publish Date: 29 September 2022