On the existence of solutions of infinite systems of Volterra-Hammerstein-Stieltjes integral equations

Abstract In this article, we deal with the solvability of an infinite system of Volterra-Hammerstein-Stieltjes integral equations in the space of continuous and bounded functions defined on <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi mathvariant="double-struck">R</m:mi> </m:mrow> <m:mrow> <m:mo>+</m:mo> </m:mrow> </m:msub> </m:math> {{\mathbb{R}}}_{+} with values in the sequence space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>l</m:mi> </m:mrow> <m:mrow> <m:mn>1</m:mn> </m:mrow> </m:msub> </m:math> {l}_{1} . We expand a known existence result for such an infinite system of integral equations and prove a theorem for a larger class of infinite systems of integral equations of this type.