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Abstract: The paper establishes a sufficient condition for the controllability of semilinear mixed Volterra–Fredholm-type integro-differential inclusions in Banach spaces. We use Bohnenblust–Karlin''s fixed point theorem combined with a strongly continuous operator semigroup. Our main condition (A5) only depends upon the local properties of multivalued map on a bounded set. An example is also given to illustrate our main results. [Copyright &y& Elsevier]

Abstract: Dhakne and Kendre [On abstract nonlinear mixed Volterra–Fredholm integro-differential equations, Presented Paper in the International Conference at IIT-Bombay, 11–13 December, 2004] has 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 typewhere 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. [Copyright &y& Elsevier]