On infinite systems of nonlinear integral equations in two variables in Banach Space $BC(\mathbb{R_+}\times \mathbb{R_+},c_0$)

In this paper, the solvability of an infinite system of integral equations of the Volterra-Hammerstein type in Banach space $BC(\mathbb{R_+}\times \mathbb{R_+},c_0$) is examined. Technique associated with the measure of noncompactness plays the most important role in adopted analysis and authors present an example to validate the applicability of the result.