Common Fixed Points for Generalized "Equation missing" -Pair Mappings on Cone Metric Spaces

Abstract

We define the concept of generalized ϕ-pair mappings and prove some common fixed point theorems for this type of mappings. Our results generalize some recent results.

Common fixed points of four mappings satisfying weakly contractive-like condition in cone metric spaces

“…An incorrect attempt to generalize the result in [4] to cone metric spaces in [8] was later correctly stated and proved in [3] and [7]. In this paper, we use a nondecreasing mapping F as in [10] to generalize the results in [1] and [2]. Furthermore, we prove a common fixed point theorem of integral type in cone metric spaces that generalizes the recent result in [3] and [7].…”

“…Definition 1.6 [6] The self mappings f and g of a cone metric space (X, d) are said to be weakly compatible if they commute at their coincidence points, that is, if f (p) = g(p) for some p ∈ X, then f (g(p)) = g(f (p)). Definition 1.7 [10] Let P be a cone and let {ω n } be a sequence in P . One says that ω n −→ 0 if for every ∈ P with 0 there exists N > 0 such that ω n for all n ≥ N .…”

“…We state in the following some special cases of our theorems: Corollary 2.3 [10] Let (X, d) be a cone metric space and let S, T : X → X be two mappings such that:…”

Coupled Coincidence Points for Generalized <img width=92 height=39 src="http:/fbpe/img/cubo/v16n2/art08-yq.jpg">-Pair Mappings in Ordered Cone Metric Spaces

“…In 2007, Huang and Zhang [5] introduced the concept of cone metric spaces and proved some important fixed point theorems. Afterwards, Sabetghadam and Masiha [17] obtained some fixed point results for generalized ϕ-pair mappings in cone metric spaces. The purpose of this paper is to obtain sufficient conditions for existence of coupled coincidence points for mappings satisfying generalized contractive conditions related to ψ and ϕ -maps in ordered cone metric spaces.…”