On Common Fixed Points and Best Approximation on Nonconvex Sets

Sumit Chandok, T. D. Narang

Abstract

By generalizing a theorem of G.Meinardus [Arch. Rational Mech.
Anal. 14(1963), 301-303], B.Brosowski [Mathematica (Cluj) 11(1969), 195-200] proved a result on invariant approximation using fixed point theory. Subsquently, many generalizations of Brosowski’s result have appeared. We also obtain several Brosowski-Meinardus type theorems for nonexpansive mappings defined on a class of nonconvex sets containing the class of starshaped sets thereby extending and generalizing various known results on the subject.