New common fixed point theorems and invariant approximation in convex metric spaces

Abstract

In this paper, we use new concepts of subcompatibility and subsequential continuity contained in (Bouhadjera, Godet-Thobie, Common fixed theorems for pairs of subcompatible maps, 17 June 2009. [math.FA]) to prove common fixed point theorems for a pair of maps in metric as well as convex metric spaces which are essentially patterned after a theorem of Huang and Li (Fixed point theorems of compatible mappings in convex metric spaces, Soochow J. Math. 22(3) (1996), 439--447). We also prove some related fixed point theorems and utilize certain such results to prove theorems on best approximation.