On existence results and qualitative properties of mild solution of semilinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces

In this paper, we prove the existence results, uniqueness, continuous dependence on initial functions and on parameters of mild solution of semilinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The closeness and continuous dependence of the mild solution on the right-hand side of the equation is also established. Our analysis is based on the theory of strongly continuous semigroup, the nonlinear alternative of Leray–Schauder and the integral inequality established by Pachpatte. An example is given to illustrate the results.