On a Volterra Integral Equation with Delay, via w -Distances

Veronica Ilea and Diana Otrocol
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Veronica Ilea: Department of Mathematics, Babeş-Bolyai University, 1 M. Kogălniceanu Street, 400084 Cluj-Napoca, Romania
Diana Otrocol: Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania

Mathematics, 2021, vol. 9, issue 18, 1-8

Abstract: The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take into account the support of w-distance and the complexity of the delay equation. Gronwall-type theorem and comparison theorem are also discussed using a weak Picard operator technique. In the end, an example is provided to support our results.

Keywords: Volterra integral equation with delay; w -distance; weakly Picard operator; abstract Gronwall lemma (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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