Fixed point theorems for a system of operator equations with applications
Keywords:
Fixed point, contractive condition, metric space, coupled fixed point, integral equation.Abstract
The purpose of this paper is to present some existence and uniqueness theorems for a general system of operator equations. The abstract result generalizes some existence results obtained in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 7347-7355] for the case of coupled fixed point problem. We also provide an application to a system of integro-differential equations.
Mathematics Subject Classification (2010): 47H10, 54H25, 34B15.
References
Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3(1922), 133-181.
Berinde, V., Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 74(2011) 7347-7355.
Krasnoselskii, M.A., Zabreiko, P.P., Geometrical Methods of Nonlinear Analysis, Springer Verlag Berlin, 1984.
Lakshmikantham, V., Ciric, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70(2009), 4341-4349.
Rus, I.A., Principles and Applications of Fixed Point Theory (in Romanian), Dacia, Cluj-Napoca, 1979.
Rus, I.A., Petrusel, A., Petrusel G., Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.
Urs, C.L., Contributions to the study of the coupled fixed point problem, Ph. D. Thesis, 2013.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2016 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
