On coupled coincidence point theorems on partially ordered G-metric spaces without mixed g-monotone

Abstract

In this work, we prove the existence of a coupled coincidence point theorem of nonlinear contraction mappings in G-metric spaces without the mixed g-monotone property and give some examples of a nonlinear contraction mapping, which is not applied to the existence of coupled coincidence point by using the mixed monotone property. We also show the uniqueness of a coupled coincidence point of the given mapping. Further, we apply our results to the existence and uniqueness of a coupled coincidence point of the given mapping in partially ordered G-metric spaces.

Fixed Point Results for Multi-Valued Mappings in G - Metric Spaces

“…The G-metric space from then on has paid the attention of mathematicians and natural philosopher and became a very popular topic especially in the sense of perspective of fixed point theory. The definition of G-metric space is as the following (see [18] and [2]- [7]): Definition 1.1. (see [2]- [7] and [18]) Let E be a nonempty set.…”

“…The definition of G-metric space is as the following (see [18] and [2]- [7]): Definition 1.1. (see [2]- [7] and [18]) Let E be a nonempty set. A function G is said a generalized metric, or a G-metric, and the pair (E, G) is called a G-metric space, For u, v, w, c ∈ E, if the function G : E × E × E → [0, +∞) satisfies the following properties [2]- [7] and [18]) Let (E, G) be a G-metric space.…”

“…(see [2]- [7] and [18]) Let E be a nonempty set. A function G is said a generalized metric, or a G-metric, and the pair (E, G) is called a G-metric space, For u, v, w, c ∈ E, if the function G : E × E × E → [0, +∞) satisfies the following properties [2]- [7] and [18]) Let (E, G) be a G-metric space. Suppose that {u n } +∞ n=1 ⊂ E be a subsequence of points.…”

“…Suppose that {u n } +∞ n=1 ⊂ E be a subsequence of points. We call that u n is G-convergent to u * ∈ E if for any ε > 0, there exists positive integer [2]- [7] and [18]…”