Abstract. The purpose of this paper is to establish a common fixed point theorem for two pairs of subcompatible single and set-valued Dmaps in a metric space. This result improves, extends and generalizes the result of [1] and others.

In this paper, in the first step, we will introduce the concept of occasionally weakly biased mappings of type (A) which is a convenient generalization of the concept of weakly biased mappings of type (A). In the second step, we will show that this new definition coincides with our concept of occasionally weakly biased mappings given in [8]. In the third and last step we will give an example which verifies the validity of our result.

The subject of this paper is to prove a common fixed point theorem for four weakly compatible maps which extends and improves Theorem 1 of [2] and others by removing the assumption of continuity and relaxing the property of compatibility to weak compatibility. Also we give another extension of the same theorem.

Abstract. A general common fixed point theorem for two pairs of weakly subsequentially continuous mappings (recently introduced) satisfying a significant estimated implicit function is proved. An extension of this result is thereby obtained. Our results assert the existence and uniqueness of common fixed points in several cases.

In this contribution, two unique common fixed point theorems for three and four self mappings are given which improve and extend the results of Aage and Salunke [1] and others.