Two extensions of coupled coincidence point results for nonlinear contractive mappings
type: Item
instance of: scholarly article
title: Two extensions of coupled coincidence point results for nonlinear contractive mappings
zbMATH Open document ID: 1331.54064
author: Shaban Sedghi
author: Poom Kumam
author: Tatjana Došenović
author: Nabi Shobe
published in: Journal of the Egyptian Mathematical Society
publication date: 2015-11-26T00:00:00Z
review text: Inspired by the notion of coupled coincidence point results due to \textit{T. G. Bhaskar} and \textit{V. Lakshmikantham} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 65, No. 7, 1379--1393 (2006; Zbl 1106.47047)] and \textit{V. Lakshmikantham} and \textit{L. Ćirić} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, 4341--4349 (2009; Zbl 1176.54032)], the authors introduce the concept of a mixed fg-monotone mapping and prove a coupled coincidence fixed point theorem (Theorem 2.4) for nonlinear contractive mappings in partially ordered complete metric spaces. The proof of the theorem is valid under the assumed conditions. A~suitable example (Example 2.5) is also given to support Theorem 2.4. One more interesting result is proved in the framework of partially ordered probabilistic metric spaces, which extends the results of \textit{L. Ćirić} et al. [Fixed Point Theory Appl. 2011, Article ID 56, 13 p. (2011; Zbl 1271.54078)] to a more general class of \(t\)-norms mentioned in Example 1.7.
reviewed by: Sunny Chauhan
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 6513990
zbMATH Keywords: partially ordered set
zbMATH Keywords: coupled coincidence point
zbMATH Keywords: mixed monotone property
zbMATH Keywords: Hadzic type t-norms
zbMATH Keywords: Menger probabilistic metric spaces
MaRDI profile type: Publication
full work available at URL: j.joems.2014.06.002
OpenAlex ID: W2070410517
cites work: Common coupled fixed point theorems in cone metric spaces for \(w\)-compatible mappings
cites work: Generalized contractions in partially ordered metric spaces
cites work: Fixed point theorems in partially ordered metric spaces and applications
cites work: On Nonlinear Contractions
cites work: Q4206101
cites work: A Generalization of Banach's Contraction Principle
cites work: Multi-valued non-self-mappings on convex metric spaces
cites work: Coincidence and fixed points for maps on topological spaces
cites work: On the steepest descent approximation method for the zeros of generalized accretive operators
cites work: Fixed point theorems for multi-valued contractions in complete metric spaces
cites work: Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces
cites work: Mixed monotone-generalized contractions in partially ordered probabilistic metric spaces
cites work: Monotone generalized contractions in partially ordered probabilistic metric spaces
cites work: Quasicontraction nonself-mappings on convex metric spaces and common fixed point theorems
cites work: Q3871678
cites work: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces
cites work: Q5479764
cites work: Common fixed point theorems for weakly isotone increasing mappings in ordered partial metric spaces
cites work: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations
cites work: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations
cites work: An application of fixed point theorems in best approximation theory
cites work: A fixed point theorem in partially ordered sets and some applications to matrix equations
cites work: Generalized weak contractions in partially ordered metric spaces
cites work: On Ciric's fixed point theorem
cites work: Coupled coincidence point theorems for \(\alpha\)-\(\psi\)-contractive type mappings in partially ordered metric spaces
cites work: Coupled coincidence point and common coupled fixed point theorems lacking the mixed monotone property
cites work: Q4920481
cites work: Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces
cites work: Statistical Metrics
cites work: Triangular norms
DOI: 10.1016/J.JOEMS.2014.06.002
description: scientific article; zbMATH DE number 6513990