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
Highlights
Introduction and PreliminariesRecent paper contains applications of fixed point of non-expansive mappings in a modular space which is known as the following: Definition 1.1 [1] Let be real linear space over, a function : is called modular if for :(i) if and only if (ii) = withIraqi Journal of Science, 2021, Vol 62, No 9, pp: 3097-3101 (iii) + if and only ifIf (iii) replaced by (iii) +, for, is called convex modular
Proof: Firstly, we prove S is self-mapping on be a mapping, and
Form (**) and T-contraction and T-non-expansive, we get which is a contraction If the hypothesis (ii) holds, i.e, if to and is demiclosed on
Summary
Introduction and Preliminaries Recent paper contains applications of fixed point of non-expansive mappings in a modular space which is known as the following: Definition 1.1 [1] Let be real linear space over , a function : is called modular if for if and only if (ii) A corresponding set is called convex modular space. Let be a convex real modular space with dual (for details of dual , see [8]) Definition 1.3 [8] [7] A sequence in is said to be weakly convergent if there is an e such that for every P
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