On the Burton method of progressive contractions for Volterra integral equations



	On the Burton method of progressive contractions for Volterra integral equations


	Fixed Point Theory, Volume 21, No. 2, 2020, 585-594, July 1st, 2020 DOI: 10.24193/fpt-ro.2020.2.41 Authors: Veronica Ilea and Diana Otrocol Abstract: In the paper [4] the author give a new method to study the existence and uniqueness of a solution on [0, ∞[ of a scalar integral equation where u, v ∈ ℝ, t ∈ [0, ∞[ imply that there exists 0 < l < 1 with and for each b > 0 there exists L_b < 0 such that In this paper we extend the Burton method to the case where instead of scalar equations we consider an equation in a Banach space. Key Words and Phrases: Progressive contractions, fixed points, existence, uniqueness, integro-differential equations. 2010 Mathematics Subject Classification: 45J05, 37C25, 47H10, 47H09. Published on-line: July 1st, 2020. Abstract pdf Fulltext pdf Back to volume's table of contents