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Solvability of infinite system of nonlinear convolution type integral equations in the tempered sequence space $m^{β} (φ, p)$

Hamid Mehravaran

Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

E-mail Address: hamid_mehravaran@mshdiau.ac.ir

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and

Hojjatollah Amiri Kayvanloo

Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

E-mail Address: amiri.hojjat93@mshdiau.ac.ir

Corresponding author.

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https://doi.org/10.1142/S1793557123500043Cited by:2 (Source: Crossref)

Abstract

In this paper, we first introduce the concept of tempered sequence space $m^{β} (φ, p)$ . Then, we construct a Hausdorff measure of noncompactness on this sequence space. Furthermore, by employing this measure of noncompactness we discuss the existence of solutions for an infinite system of nonlinear convolution differential equations in the tempered sequence space $m^{β} (φ, p)$ . Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result.

Communicated by R. T. Tan

Keywords:

AMSC: 47H09, 47H10, 34A12

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