Coupled fixed point theorems for \((\varphi,\psi)\)-contractive mixed monotone mappings in partially ordered metric spaces and applications
type: Item
instance of: scholarly article
title: Coupled fixed point theorems for \((\varphi,\psi)\)-contractive mixed monotone mappings in partially ordered metric spaces and applications
zbMATH Open document ID: 1390.54045
DOI: 10.1155/2014/586096
author: Manish Jain
author: Neetu Gupta
author: Sanjay Kumar
published in: International Journal of Analysis
publication date: 2018-06-11T00:00:00Z
review text: Summary: The object of this paper is to establish the existence and uniqueness of coupled fixed points under a \((\varphi,\psi)\)-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of \textit{V. Berinde} [Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 18, 7347--7355 (2011; Zbl 1235.54024); ibid. 75, No. 6, 3218--3228 (2012; Zbl 1250.54043)] and weakens the contractive conditions involved in the well-known results of \textit{T. G. Bhaskar} and \textit{V. Lakshmikantham} [ibid. 65, No. 7, 1379--1393 (2006; Zbl 1106.47047)], and \textit{Nguyen Van Luong} and \textit{Nguyen Xuan Thuan} [ibid. 74, No. 3, 983--992 (2011; Zbl 1202.54036)]. The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54E40
Mathematics Subject Classification ID: 54F05
zbMATH DE Number: 6883058
zbMATH Keywords: \((\varphi,\psi)\)-contractive condition
zbMATH Keywords: coupled fixed point theorem
Wikidata QID: Q59041406
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/586096
OpenAlex ID: W2037127519
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description: scientific article; zbMATH DE number 6883058