Attractivity results for a nonlinear functional integral equation

In this paper two existence results concerning the global attractivity and global asymptotic attractivity for a certain functional nonlinear integral equation are proved. Our existence results include several existence and attractivity results obtained earlier by Darwish and Hu–Yan as special cases under weaker conditions. A fixed point theorem of Dhage is used in formulating our main results and the characterizations of solutions are obtained in the space of functions defined, continuous and bounded on unbounded intervals.