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An extension of coupled fixed point’s concept in higher dimension and applications. (English) Zbl 1247.54048
Summary: We introduce the concept of fixed point of $N$-order for mappings $F:{X}^{N}\to X$, where $N\ge 2$ and $X$ is an ordered set endowed with a metric $d$. We establish fixed point results for such mappings satisfying a given contractive condition. The presented theorems extend and generalize the coupled fixed point results of T. G. Bhaskar and V. Lakshmikantham, Nonlinear Anal., Theory Methods Appl. 65, No. 7, A, 1379–1393 (2006; Zbl 1106.47047)] and the tripled fixed point results of V. Berinde and M. Borcut, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 15, 4889–4897 (2011; Zbl 1225.54014)]. Some applications to integral equations and to matrix equations are also presented in this work.
##### MSC:
 54H25 Fixed-point and coincidence theorems in topological spaces 47H10 Fixed point theorems for nonlinear operators on topological linear spaces 45G10 Nonsingular nonlinear integral equations