Solvability of infinite system of nonlinear convolution type integral equations in the tempered sequence space mβ(φ,p)

Abstract

In this paper, we first introduce the concept of tempered sequence space [Formula: see text]. 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 [Formula: see text]. Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result.