Summary: M. B. Dhakne and S. D. Kendre [Commun. Appl. Nonlinear Anal. 13, No. 4, 101–112 (2006; Zbl 1119.45005)] have proved the existence of the abstract nonlinear mixed Volterra-Fredholm integro-differential system of the type
In this short article, we have studied sufficient conditions for controllability of semi-linear mixed Volterra-Fredholm-type integro-differential systems in Banach space of the type
where the state takes values in a Banach space and the control function is given in , with as a Banach space. Here is the infinitesimal generator of a strongly continuous semigroup in a Banach space . is a bounded linear operator from into . The result is obtained by using the application of the topological transversality theorem known as Leray-Schauder alternative and rely on a priori bounds of solutions. An example is provided to illustrate the theory.