Existence of solutions of infinite systems of integral equations in the Frechet spaces

Arab, Reza; Allahyari, Reza; Shole Haghighi, Ali

doi:10.22075/ijnaa.2017.1074.1222

Existence of solutions of infinite systems of integral equations in the Frechet spaces

Document Type : Research Paper

Authors

Reza Arab ¹

Reza Allahyari ²

Ali Shole Haghighi ³

¹ Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran

² Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

³ Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.

10.22075/ijnaa.2017.1074.1222

Abstract

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tychonoff fixed point theorem. Also, we present an example of nonlinear integral equations to show the efficiency of our results. Our results extend several comparable results obtained in the previous literature.

Keywords

Measure of noncompactness

Frechet space

Tychonoff fixed point theorem

Infinite systems of equations