The existence of asymptotically stable solutions for a nonlinear functional integral equation with values in a general Banach space

Motivated by the recent known results about the solvability and existence of asymptotically stable solutions for nonlinear functional integral equations in spaces of functions defined on unbounded intervals with values in the nn-dimensional real space, we establish asymptotically stable solutions for a nonlinear functional integral equation in the space of all continuous functions on R+R+ with values in a general Banach space, via a fixed point theorem of Krasnosel’skii type. In order to illustrate the result obtained here, an example is given.