Fixed Point Theorems via Absorbing Maps

U. Mishra, A. S. Ranadive, D. Gopal

Abstract

The purpose of this paper is to obtain common fixed point theorems by using a new notion of absorbing maps in fuzzy metric space. In this paper we illustrate the properties of absorbing maps. Moreover we demonstrate the necessity of absorbing maps to find a common fixed point in fuzzy metric spaces and menger spaces. Our result generalizes many known results and explore the possibility of applying the notion of reciprocal continuity and absorbing maps to the problem of finding common fixed points of four mappings or sequence of mappings satisfying contractive type conditions in fuzzy metric spaces as well as probabilistics metric spaces without being continuous even at the fixed point.