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Open Access Article
1 - Solving infinite system of nonlinear integral equations by using F-generalized Meir-Keeler condensing operators, measure of noncompactness and modified homotopy perturbation.
mohsen rabbani Reza ArabIn 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 MoreIn 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. Manuscript profile -
Open Access Article
2 - New operators through measure of non-compactness
M. Rabbani ‎R. Arab A.A. Tabatabai AdnaniIn 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 equa MoreIn 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 papers such as [7, 11]. By the above concepts we can generalize some theorems which was proved by other authors, especially Darbo’s fixed point theorem. The space of our solution contains of all convergence sequences with a finite limit, such that with suitable norm is a Banach space. To reach our subject, we prove some theorems by using measure of non-compactness and Meir-Keeler condensing operators to generalize some theorems which are created by some authors. For validity and application of our proposed theorems, we prove existence of solution for infinite system of second order differential equations with boundary conditions. Manuscript profile
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