We present a counterexample to the main result of the abovementioned paper showing that this result is false and cannot be improved in a simple way.
Krzysztof A. Topolski. "Comment on “Existence Theorem for Integral and Functional Integral Equations with Discontinuous Kernels”." Abstr. Appl. Anal. 2015 1 - 3, 2015. https://doi.org/10.1155/2015/698121