Solvability of the infinite systems of nonlinear third-order differential equations in the weighted sequence space ${\bf m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}, \psi,q)}$
Subject Areas : Fixed point theory
M. Khanehgir
1
(Department of Mathematics, Mashhad Branch, Islamic Azad
University, Mashhad, Iran)
H. Amiri Kayvanloo
2
(Department of Mathematics, Mashhad Branch, Islamic Azad
University, Mashhad, Iran)
R. Allahyari
3
(Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran)
M. Mehrabinezhad
4
(Department of Mathematics, Mashhad Branch, Islamic Azad
University, Mashhad, Iran)
Keywords: Infinite system of third-order boundary value problem, measure of noncompactness, Meir-Keeler condensing operator, weighted sequence space,
Abstract :
In this work, we first introduce the concept of weighted sequence space $m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}, \psi,q)$. Then, we construct a Hausdorff measure of noncompactness on this sequence space. Furthermore, by employing this measure of noncompactness we discuss the solvability of an infinite system of nonlinear third-order differential equations with initial conditions in the weighted sequence space $m_\omega(\Delta_{\mathfrak{v}}^{\varsigma}, \psi,q)$. Eventually, we demonstrate an example to show the usefulness of the obtained result.
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