Fixed point theorems for compatible and subsequentially continuous mappings in Menger spaces

Abstract

In the present paper, we prove common fixed point theorems using the notions of compatibility and subsequentially continuity (alternately subcompatibility and reciprocally continuity) in Menger spaces. We also give a common fixed point theorem satisfying an integral analogue. As applications to our results, we obtain the corresponding fixed point theorems in metric spaces. Some illustrative examples are also given which demonstrate the validity of our results.