On Invariant Approximations in Modular Spaces

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

Common fixed point and best approximation for Banach operator pairs in non-starshaped domain

Common fixed point results for Banach operator pair with generalized nonexpansive mappings in non-starshaped domain of metric space have been obtained in the present work. As application, more general best approximation results in normed space have also been determined. These results extend and generalize various existing known results with the aid of Banach operator pair and without starshaped condition of domain.