No abstract

Abstract. In this paper, we obtain a generalized common fixed point theorem for four mappings using the conditions of non-compatibility and faint compatibility.

In this paper we establish a common fixed point theorem for two maps under the generalized contractive condition in a complete metric spaces.

In this paper we define the concept of conditionally commuting mappings and establish some common fixed point theorems for hybrid pair of mappings satisfying a nonexpansive type condition.

The main objective of the paper is to prove some unified common fixed point theorems for a family of mappings under a minimal set of sufficient conditions. Our results subsume and improve a host of common fixed point theorems for contractive type mappings available in the literature of the metric fixed point theory. Simultaneously, we provide some new answers in a general framework to the problem posed by Rhoades (Contemp Math 72, 233-245, 1988) regarding the existence of a contractive definition which is strong enough to generate a fixed point, but which does not force the mapping to be continuous at the fixed point. Concrete examples are also given to illustrate the applicability of our proved results.