Solving infinite system of nonlinear integral equations by using ‎F-‎generalized Meir-Keeler condensing operators, measure of noncompactness and modified homotopy perturbation.

Subject Areas : Statistics

mohsen rabbani ¹ , Reza Arab ²

1 - Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.
2 - Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran.

Received: 2017-09-04 Accepted : 2018-08-06 Published : 2018-08-01

Keywords: هموتوپی اختلا لات, فضای با ناخ, معادلات انتگرال, اندازه نافشردگی, عملگرتراکمی مر-کلر,

Abstract :

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we prove some fixed point theorems. With the help of the above process we try to generalize some theorems which were proved by other authors such as [3, 19] about existence of solution by fixed point theorems. Then for validity and application‎ of our proposed theorems, we prove existence of solution for infinite system of nonlinear integral equations. Finally for ability and more attractiveness of this research, we construct an iteration algorithm by modified homotopy perturbation and Adomian decomposition method to obtain approximation of solution of the infinite system of nonlinear integral equations.