Volterra theory on time scales
type: Item
instance of: scholarly article
title: Volterra theory on time scales
zbMATH Open document ID: 1295.45001
published in: Results in Mathematics
publication date: 2014-06-18T00:00:00Z
review text: Time scales theory was introduced by \textit{S. Hilger} [Result. Math. 18, No. 1--2, 18--56 (1990; Zbl 0722.39001)]. The objective of this theory is to unify the discrete and the differential calculus. This paper addresses generalized Volterra integral equations on time scales. It is reported that the continuity property can be relaxed for the kernel function. That is because the author employs the method to guarantee existence and uniqueness which does not make use of the Banach fixed-point theorem. For more results on the Volterra equations with piecewise continuous kernels, the readers may refer to \textit{D. N. Sidorov} [Differ. Equ. 49, No. 2, 210--216 (2013); translation from Differ. Uravn. 49, No. 2, 209--215 (2013; Zbl 1348.45002)]. The paper also covers results concerning the reciprocity property of kernels and Picard iterates.
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 26E70
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6305232
zbMATH Keywords: Volterra integral equations
zbMATH Keywords: time scales
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: resolvent kernel
author: Basak Karpuz
reviewed by: Denis Sidorov
MaRDI profile type: Publication
full work available at URL: s00025-013-0344-4
OpenAlex ID: W1997709749
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DOI: 10.1007/S00025-013-0344-4
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description: scientific article; zbMATH DE number 6305232