New Unique Common Fixed Point Results for Four Mappings with Ф-Contractive Type in 2-Metric Spaces

Abstract

In this paper, some new unique common fixed points for four mappings satisfying Ф-contractive conditions on noncomplete 2-metric spaces are obtained, in which the mappings do not satisfy continuity and commutation. The main results generalize and improve many well-known and corresponding conclusions in the literatures.

Common Fixed Points for a Countable Family of Set-Valued Mappings with Quasi-Contractive Conditions on Metrically Convex Spaces

“…Similar results for multi-valued mappings were respectively given by Assad [2] and Assad and Kirk [3]. On the other hand, many authors discussed common fixed point problems [4][5][6][7] for finite single or multi-valued mappings on a complete 2-metric convex space or a complete cone metric space respectively. And some authors also discussed common fixed point problems [8][9][10][11][12][13] for a countable family of self-single-valued mappings with contractive or quasi-contractive conditions on a metric space or a metrically convex space respectively.…”

Common Fixed Points for Two Mappings With Expansive Properties on Complex Valued Metric Spaces

“…( [10]) Let f, g : X → X be weakly compatible. If f and g have a unique point of coincidence, that is, there exist an element x ∈ X and a unique element w ∈ X satisfying w = f x = gx, then w is the unique common fixed point of f and g. In this case, x is said to be a coincidence point of f and g, w is said to be a point of coincidence of f and g.…”

Unique Common Fixed Point in b2 Metric Spaces

“…The author in (see [6]) gets the coincidence and common fixed point theories in 2 metric spaces (see [7] [8] [9]), using the method in (see [1] [2] [3]). In this paper, a known existence theorems of common fixed points for two mappings satisfying expansive conditions in 2 b metric space (see [10]), which is the generalization of both 2 metric space and b metric space (see [11] [12] 2) ( ) ( )…”

“…Definition 2.2. [7] [8] [9] Let X be an nonempty set and let : d X X X × × →  be a map satisfying the following conditions: 1) For every pair of distinct points , x y X ∈ , there exists a point z X ∈ such that ( )…”