An extension of coupled fixed point’s concept in higher dimension and applications

Martínez-Moreno

Journal of Mathematical Analysis and Applications

2012

a b s t r a c tIn this paper we propose a notion of coincidence point between mappings in any number of variables and we prove some existence and uniqueness fixed point theorems for nonlinear mappings verifying different kinds of contractive conditions and defined on partially ordered metric spaces. These theorems extend and clarify very recent results that can be found in [T. Gnana-Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7)(2006) 1379-1393], [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889-4897] and [M. Berzig, B. Samet, An extension of coupled fixed point's concept in higher dimension and applications, Comput. Math. Appl. 63 (8) (2012) 1319-1334].

Section: Introductionmentioning

confidence: 92%

Multidimensional fixed point theorems in partially ordered complete metric spaces

Martínez-Moreno

Journal of Mathematical Analysis and Applications

2012

Journal of the Korean Mathematical Society

“…The above definition is a generalization of m-mixed monotone property for the mapping F : X n → X introduced by M. Berzig and B. Samet [5], where n ≥ 2 and 1 ≤ m < n. Definition 2.2. Let X be a nonempty set, n(≥ 2) a positive integer, I and J nonempty disjoint subsets of S = {1, 2, .…”

Section: Extended Notions Of Mixed Monotone Mapping and Fixed Pointmentioning

confidence: 99%

Multivariate Coupled Fixed Point Theorems on Ordered Partial Metric Spaces

Lee¹,

Kim²

2014

Abstract. A partial metric, also called a nonzero self-distance, is motivated by experience from computer science. Besides a lot of properties of partial metric analogous to those of metric, fixed point theorems in partial metric spaces have been studied recently. We establish several kinds of extended fixed point theorems in ordered partial metric spaces with higher dimension under generalized notions of mixed monotone mappings.

Journal of Nonlinear Analysis and Application

“…As a natural extension, Karapinar [17] studied the quadruple case. Very recently, the concept of multidimensional fixed/coincidence point introduced by Roldan et al in [29], which is an extension of Berzig and Samet's notion given in [5], which extended and generalized the mentioned fixed point results to higher dimensions. However, they used permutations of variables and distinguished between the first and the last variables.…”

Section: Introductionmentioning

confidence: 96%

Multidimensional coincidence point results for generalized $(\psi ,\theta ,\varphi)$-contraction on ordered metric spaces

Deshpande¹,

Handa²

2017

The main objective of this research article is to establish some coincidence point theorem for g-non-decreasing mappings under generalized (ψ, θ , φ)-contraction on a partially ordered metric space. Furthermore, we show how multidimensional results can be seen as a simple consequences of our unidimensional coincidence point theorem. Our results modify, improve, sharpen, enrich and generalize various known results.