On the solution of a system of integral equations via matrix version of Banach contraction principle

Muhammad Usman Ali, Tayyab Kamran, Hassan Houmani, Mihai Postolache


The purpose of this paper is to extend Perov's fixed point theorem in the setting of  modular generalized metric space, which is also establish in this article. Further we discuss the Perov's result in the setting of two modular generalized metric spaes. As an application we prove the existence of solution for a system of integral equations.


Generalized metric space; modular generalized metric space; modular metric space

Full Text:



bibitem{Perov} A.I. Perov, On the Cauchy problem for a system of ordinary differential equations, Pviblizhen. Met. Reshen. Differ. Uvavn., 2 (1964), 115-134.

bibitem{Varga} R.S. Varga, Matrix Iterative Analysis, Springer Series in Computational Mathematics, Springer, Berlin, Germany, 27 (2000).

bibitem {Filip} A.D. Filip, A. Petrusel, Fixed point theorems on spaces endowed with vector-valued metrics, Fixed Point Theory Appl. 2010 (2010), Article ID 281381.

bibitem{Rus} I.A. Rus, Principles and Applications of the Fixed Point Theory, Dacia, Cluj-Napoca, Romania, (1979).

bibitem{Turinici} M. Turinici, Finite-dimensional vector contractions and their fixed points, Studia Universitatis Babes-Bolyai Mathematica, 35 (1990), 30-42.

bibitem {Bucur} A. Bucur, L. Guran, A. Petrusel, Fixed points for multivalued operators on a set endowed with vector-valued metrics

and applications, Fixed Point Theory 10(2009), 19-34.

bibitem {Regan} D. O'Regan, N. Shahzad, R.P. Agarwal, Fixed Point Theory for Generalized Contractive Maps on Spaces with Vector-Valued Metrics. Fixed Point Theory and Applications, Nova Science Publishers, New York (2007) 143-149.

bibitem{Chistyakov1} V.V. Chistyakov, Modular metric spaces I basic concepts, Nonlinear Anal., 72 (2010), 1-14.

bibitem{Khamsi1} A.A.N. Abdou, M.A. Khamsi, Fixed points of multivalued contraction mappings in modular metric spaces, Fixed Point Theory App. (2014), 2014:249.

bibitem{Alfuraidan} M.R. Alfuraidan, Fixed points of multivalued

contraction mappings in modular metric spaces, Fixed Point Theory

Appl., (2015), 2015:46.

bibitem{Kumam1} P. Chaipunya, C. Mongkolkeha, W. Sintunavarat, P. Kumam, Fixed point theorems for multivalued mappings in modular metric spaces, Abstr. Appl. Anal., (2012), 2012 Article ID 503504.

bibitem{Chistyakov2} V. V. Chistyakov, Fixed points of modular

contractive maps, Doklady Math., 86 (2012), 515-518.

bibitem{Khamsi3} M. A. Khamsi, W. M. Kozlowski

Fixed Point Theory in Modular Function Spaces, Birkhauser (2015).


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905