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

Abstract

Abstract. 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. IntroductionFixed point theorems have been applied in the field of invariant approximation theory since last four decades and several interesting and valuable results have been studied. Meinardus [17] was the one to employ a fixed-point theorem of Schauder to establish the existence of an invariant approximation. Further, Brosowski [2] obtained a celebrated result and generalized the Meinardus's result. Later, several results [7,25,27]