Mixed g-monotone property and quadruple fixed point theorems in partially ordered metric spaces

Abstract

In this manuscript, we prove some quadruple coincidence and common fixed point theorems for F : X 4 X and g : X X satisfying generalized contractions in partially ordered metric spaces. Our results unify, generalize and complement various known results from the current literature. Also, an application to matrix equations is given. 2000 Mathematics subject Classifications: 46T99; 54H25; 47H10; 54E50.

Fixed Point Theory in Metric Type Spaces

“…In this section, we show how to reduce to the unidimensional case a version Theorem 2.1 given in [145] by Mustafa. In the original theorem, given a G-metric space .X; G/ and two mappings F W X 4 ! X and g W X !…”

Last remarks on G-metric spaces and related fixed point theorems

“…Proof Exactly as in the proof of Theorem 4.1, condition (42) implies that {x n } is right-Cauchy, and condition (43) guarantees that {x n } is left-Cauchy. By Remark 2.3, {x n } is Cauchy.…”

Quadruple fixed point theorems under (φ,ψ )-contractive conditions in partially ordered G -metric spaces with mixed g -monotone property

“…In [5], the authors first introduced the concepts of mixed monotone property and quadruple fixed point for F : X 4 → X and several quadruple fixed point theorems have been proved in partially ordered metric spaces. Afterwards, a quadruple fixed point in partially ordered metric spaces is developed and related fixed points are obtained (see [6,7,8,9,10,16]). In [16], the authors first introduced the concepts of g-mixed monotone property and quadruple coincidence point for F : X 4 → X and g : X → X and several quadruple coincidence point theorems have been proved in partially ordered metric spaces.…”

“…Afterwards, a quadruple fixed point in partially ordered metric spaces is developed and related fixed points are obtained (see [6,7,8,9,10,16]). In [16], the authors first introduced the concepts of g-mixed monotone property and quadruple coincidence point for F : X 4 → X and g : X → X and several quadruple coincidence point theorems have been proved in partially ordered metric spaces. Then, in [18], Mustufa proved quadruple coincidence point in partially ordered G-metric spaces using (φ − ψ) contractions.…”

“…Definition 1.14. ( [16]) Let (X, ) be a partially ordered set and F : X 4 → X and g : X → X be two mappings. We say that F has the mixed-g-monotone property if F (x, y) is g-monotone nondecreasing in x, z and it is g-monotone nonincreasing in y, w, that is, for any x, y, z, w ∈ X, we have:…”