On Invariant Approximations in Modular Spaces

Abstract

This article is devoted to presenting results on invariant approximations over a non-star-shsped weakly compact subset of a complete modular space by introduced a new notion called S-star-shaped with center f: if be a mapping and , . Then the existence of common invariant best approximation is proved for Banach operator pair of mappings by combined the hypotheses with Opial’s condition or demi-closeness condition

افضل تقريب في فضاءات b - المعيارية

“…Definition 6 16 A set-valued mapping 𝐹 is 𝑢. 𝑠. 𝑐., if the set {𝑢 𝛬 ∈ 𝛤 𝜁 : 𝐹(𝑥) ∩ 𝐵 ≠ ∅} is closed whenever 𝐵 is closed subset of 𝑁 𝜌 . In natural way, the following are defined, see 14…”

“…It was then redefined with some modification by Musielak and Ortiz in 1959 In 2017, the best approximation modular spaces have been defined by Abed 8 and results about proximinal set, Chebysev set are proven also, see 9 . Various results in modular spaces and other related spaces about fixed point problem can be seen in Turkoglu and Nesrin 9 , Albundi 10 , Abdul Jabbar and Abed 11,12 , Ahmed 13 , Mohammed and Abed 14 , Pathak and Beg 15 , Abed and Abdul Jabbar 16,17 , Ege and, Alac 18 also Abed and Salman 19 .…”