Application of measure of noncompactness for solvability of the infinite system of integral equations in two variables in \(\ell _{p} \) \((1<p< \infty)\) (Q1736962)

Since the pioneering work of G. Darbo and B. N. Sadovskij, measures of noncompactness and condensing operators have found a wealth of interesting applications, mainly to differential equations and integral equations in normed function spaces. An application-oriented survey of such applications may be found in [\textit{J. Appell}, Fixed Point Theory 6, No. 2, 157--229 (2005; Zbl 1102.47041)]. In this paper the authors apply the notion of so-called Meir-Keeler condensing operators [\textit{A. Aghajani} et al., Acta Math. Sci., Ser. B, Engl. Ed. 35, No. 3, 552--566 (2015; Zbl 1340.47103)] to solve an infinite system of integral equations of two variables in the sequence space $l_p$ for $1<p<\infty$. They also give a (rather artificial) example, but no application which illustrates the usefulness of their result.