Coupled fixed point theorems with respect to binary relations in metric spaces

Asgari, Mohammad Sadegh¹ ; Mousavi, Baharak¹

¹ Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran

Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 2, p. 153-162.

Résumé

In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed to hold on elements that are comparable in the binary relation. Next on the basis of the coupled fixed point theorems, we prove the existence and uniqueness of positive definite solutions of a nonlinear matrix equation.

Détail

DOI : 10.22436/jnsa.008.02.07

Classification : 47H10, 15A24, 54H25
Keywords: Coupled fixed point, reflexive relation, matrix equations, positive define solution.

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