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

We introduce the concept of fixed point of NN-order for mappings F:XN→XF:XN→X, where N≥2N≥2 and XX is an ordered set endowed with a metric dd. 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.