Solvability of a recursive functional equation in the sequence Banach space

Autores: J. A. Caballero, Jackie Harjani , B.L. López, Kishin Sadarangani
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 22, Nº 2, 2007 (Ejemplar dedicado a: Banach space theory: classical topics and new directions. Cáceres 2006), págs. 147-156
Idioma: inglés
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Resumen
- 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.