Abstract
In this paper, tripled coincidence points of mappings satisfying some nonlinear contractive conditions in the framework of partially ordered -metric spaces are obtained. Our results extend the results of Aydi et al. (Fixed Point Theory Appl., 2012:101, 2012, doi:10.1186/1687-1812-2012-101). Moreover, some examples of the main result are given. Finally, some tripled coincidence point results for mappings satisfying some contractive conditions of integral type in complete partially ordered -metric spaces are deduced. MSC: 47H10, 54H25.
Highlights
Introduction and preliminariesThe concepts of mixed monotone mapping and coupled fixed point were introduced in [ ] by Bhaskar and Lakshmikantham
We present some definitions and propositions in a Gb-metric space
We present some tripled coincidence point results in ordered Gb-metric spaces
Summary
Introduction and preliminariesThe concepts of mixed monotone mapping and coupled fixed point were introduced in [ ] by Bhaskar and Lakshmikantham. (G-metric space, [ ]) Let X be a nonempty set and G : X → R+ be a function satisfying the following properties: (G ) G(x, y, z) = iff x = y = z; (G ) < G(x, x, y) for all x, y ∈ X with x = y; (G ) G(x, x, y) ≤ G(x, y, z) for all x, y, z ∈ X with z = y; (G ) G(x, y, z) = G(x, z, y) = G(y, z, x) = · · · (symmetry in all three variables); (G ) G(x, y, z) ≤ G(x, a, a) + G(a, y, z) for all x, y, z, a ∈ X (rectangle inequality). We obtain some tripled coincidence point theorems for nonlinear (ψ, φ)weakly contractive mappings in partially ordered Gb-metric spaces.
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