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

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• 作者：Maher Berzig ^{maher.berzig@gmail.com} ; Bessem Samet ; ^{bessem.samet@gmail.com} ; ^{contact@bessem.com}
• 关键词：Fixed point of N-order ; m-mixed monotone property ; Ordered metric space ; Integral equations ; Matrix equations
• 刊名：Computers and Mathematics with Applications
• 出版年：2012
• 期刊代码：37_08981221
• 类别：cp
• 出版时间：April, 2012
• 卷：63
• 期：8
• 页码：1319-1334
• 文件大小：270 K

摘要

We introduce the concept of fixed point of -order for mappings , where and is an ordered set endowed with a metric . We establish fixed point results for such mappings satisfying a given contractive condition. Presented theorems extend and generalize the coupled fixed point results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393] and the tripled fixed point results of Berinde and Borcut [V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 4889-4897]. Some applications to integral equations and to matrix equations are also presented in this work.