Common fixed points of compatible mappings

Abstract

ABSTRACT.In this paper, we present a common fixed point theorem for compatible mappings, which extends the results of Ding, Divlccaro-Sessa and the third author.

Common fixed point theorems for six self-maps in b -metric spaces with nonlinear contractive conditions

“…By using the compatible and weak compatible conditions, we prove some new common fixed point theorems for six self-maps satisfying a class of φ-type contraction condition. Because of the metric space is a special case of the b-metric space, our results presented in this paper extend and improve some well-known corresponding results in the literature due to Kang et al [12], Roshan et al [18], Jungck [10], Diviccaro and Sessa [8], and Ding [7]. for all x, y, z ∈ X.…”

“…Theorems 2.1 and 2.2 improve and extend the corresponding results of Kang et al [12] in its three aspects:…”

“…In 1990, Kang et al [12] applied the compatibility of mappings to prove common fixed point theorem of ϕ-contractive mappings. The same year, Liu [15] introduced the notion of weak compatibility of mappings and proved some common fixed point theorems.…”

A Common Fixed Point Theorem for Compatible Mappings

“…Now, we prove a common fixed point theorem which improves and extends Theorem 2.1 for compatible mappings. Also our theorem improves Theorem 2.2 from [4].…”

Compatible mappings of type (B) and common fixed point theorems in Saks spaces

“…Similarly, since B and T are compatible mappings of type (B), we have Bw = T w. Now we prove that Aw = w. If Aw = w, then by (3.2) we have Remark 4.1. Since it is possible to replace the condition of commuting mappings, weakly commuting mappings, compatible mappings, or compatible mappings of type (A) by compatible mappings of type (B), Theorem 4.1 extends, generalizes and improves a number of fixed point theorem already known in ordinary metric spaces ( [4], [5], [7], [9], [14] and [17]), and in Saks spaces ( [18] and [19]). …”