Fixed points for occasionally weakly biased mappings of type (A)

Abstract

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.

Unique common fixed points through a unified condition

“…In the paper [6] submitted in October 2009 and published in 2012, we introduced the concept of occasionally weakly biased maps which represented a generalization of weakly biased maps. Further, we used this concept to show the existence and uniqueness of common fixed points for maps satisfying different contractive conditions in a normed as well as a metric space.…”

A unique common fixed point for contractive mappings under a new concept

“…In 2012, in [5], we introduced the concept of occasionally weakly biased mappings which is a legitimate generalization of weakly biased mappings given by Jungck and Pathak in [9]. Definition 6.…”

“…Definition 6. ( [5]) Let f and g be self-mappings of a set X. The pair (f, g) is said to be occasionally weakly f -biased and g-biased, respectively, if and only if, there exists a point p in X such that f p = gp implies…”