List of Articles Measure of noncompactness

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  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 Arab
  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 More

  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. Manuscript profile
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  2 - Some generalizations of Darbo's theorem for solving a systems of functional-integral equations via measure of noncompactness
  Jamal Rezaei Roshan
  In this paper, using the concept of measure of noncompactness, which is a very useful and powerful tools in nonlinear functional analysis, metric fixed point theory and integral equations, we introduce a new contraction on a Banach space. For this purpose by using of a More

  In this paper, using the concept of measure of noncompactness, which is a very useful and powerful tools in nonlinear functional analysis, metric fixed point theory and integral equations, we introduce a new contraction on a Banach space. For this purpose by using of a measure of noncompactness on a finite product space, we obtain some generalizations of Darbo’s fixed-point theorem. Then, with the obtained results, we present some theorems on the existence of coupled fixed point for a class of operators in a Banach space. Our results generalize and extend a lot of comparable results in the literature. Also as an application, we study the existence of solution for a class of the system of nonlinear functional integral equations, which the functions and operators in the related integral operators, satisfies in a particular contraction. Finllay a concrete example is also included, which demonstrates the applicability of the obtaind results. Manuscript profile
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  3 - Solvability of infinite systems of differential equations of general order in the sequence space $bv_{\infty}$
  M. H. Saboori M. Hassani R. Allahyari
  10.30495/jlta.2023.1992240.1577
  We introduce the Hausdorff measure of noncompactness in the sequence space $bv_{\infty}$ and investigate the existence of solution of infinite systems of differential equations with respect to Hausdorff measure of noncompactness. Finally, we present an example to defend More

  We introduce the Hausdorff measure of noncompactness in the sequence space $bv_{\infty}$ and investigate the existence of solution of infinite systems of differential equations with respect to Hausdorff measure of noncompactness. Finally, we present an example to defend of theorem of existential. Manuscript profile
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  4 - Solvability of the infinite systems of nonlinear third-order differential equations in the weighted sequence space ${\bf m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}‎, ‎\psi,q)}$
  M. Khanehgir H. Amiri Kayvanloo R. Allahyari M. Mehrabinezhad
  10.30495/jlta.2023.1980047.1539
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