Reza Arab
Department of Mathematics, Sary Branch, Islamic Azad University, Sary, Iran.
[ 1 ] - Solving infinite system of nonlinear integral equations by using F-generalized Meir-Keeler condensing operators, measure of noncompactness and modified homotopy perturbation.
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...
[ 2 ] - New operators through measure of non-compactness
In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...
[ 3 ] - Solvability of infinite system of nonlinear singular integral equations in the C(Itimes I, c) space and modified semi-analytic method to find a closed-form of solution
In this article, we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I times I, c)$ by applying measure of noncompactness and Meir-Keeler condensing operators. By presenting an example, we have illustrated our results. For validity of the results we introduce a modified semi-analytic method in the case of tw...
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