On integral operators and nonlinear integral equations in the spaces of functions of bounded variation

In this paper we introduce new conditions on a kernel of a linear Fredholm integral operator which turn out to be sufficient and necessary for that operator to map the space of functions of bounded variation in the sense of Jordan into itself. Furthermore, we apply those conditions to deal with the problem of the existence of solutions to nonlinear Hammerstein equations in that space. To achieve our goals we will use a topological degree approach as well as a fixed point approach.