Solvability of systems of Volterra integral equations of the fourth kind. I (Q1874952)

The author considers the solvability of systems of Volterra integral equations of the fourth kind. These equations may be unfamiliar to the reader and therefore the paper begins with a review of equations of the first, second and third kinds. Following a sequence of lemmas in which new basic theoretical results are derived, the author gives theorems, under various conditions, that show the existence and uniqueness of solutions to fourth kind systems. In one or two places, reference to the original Russian version of the article helps clarify the English translation.