of Functions of Bounded Variation J. Matute Received: October 9, 2013; Revised: May 27, 2014; Accepted: May 29, 2014 Abstract. In this paper we use a Leray-Schauder alternative in order to prove the existence and uniqueness of solutions for the Volterra equation in the Banach space of functions of bounded variation. Keywords: Volterra integral equation; existence and uniqueness of solutions; functions of bounded variation. AMS Subject classification: Primary: 45D05, 26B30. ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |