Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space

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 [GRAPHIC] x(0) = x(0) is an element of X; t is an element of J = [0,T] In this short article, we have studied sufficient conditions for controllability of semi-linear mixed Volterra-Fredhoim-type integro-differential systems in Banach space of the type [GRAPHICS] x(0) = x(0), t is an element of J = [0, T] where the state x(.) takes values in a Banach space X and the control function u(.) is given in L-2(J, U), with U as a Banach space. Here A is the infinitesimal generator of a strongly continuous semigroup in a Banach space X. B is a bounded linear operator from U into X.