Resumen de Solvability of a recursive functional equation in the sequence Banach space

J. A. Caballero, Jackie Harjani , B.L. López, Kishin Sadarangani

• The main aim of this paper is to study the existence of solutions of the following recursive functional equation x(n) = f(n, x(n), x(n - 1)) in the space l2, under general assumptions. The main tools of our existence theorem are the characterization of the relatively compact sets in the space l2 and Schauder Fixed point theorem. Moreover, our functional equation has as particular cases some integral equations of Urysohn type. Finally, we present some examples where our theorem can be applied.