Fixed Points of Quasi-Nonexpansive Mappings and Best Approximation

Using fi xed point theory, B. Brosowski [Mathematica (Cluj) 11(1969), 195-220] proved that if T is a nonexpansive linear operator on a normed linear space X, C a T-invariant subset of X and x a T-invariant point, then the set PC(x) of best C-approximant to x contains a T-invariant point if PC(x) is non-empty, compact and convex. Subsequently, many generalizations of the Brosowski s result have appeared. In this paper, we also prove some extensions of the results of Brosowski and others for quasi-nonexpansive mappings when the underlying spaces are metric linear spaces or convex metric spaces.