COMMON FIXED POINT OF SUBCOMPATIBLE MAPPINGS AND BEST APPROXIMATIONS IN CONVEX METRIC SPACES

In this paper, we first establish a common fixed point theorem for a pair of compatible mappings satisfying a Ciric's type contraction condition in the setting of convex metric spaces which is utilized to derive new common fixed point result for subcompatible maps under suitable assumptions. Subsequently, as applications to new common fixed point result, we derive invariant approximation results. Several related results are also derived as corollaries to our main results besides furnishing illustrative examples to demonstrate the validity of the hypotheses of our results proved herein.