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


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.


Veronica Ilea
Department of Mathematics, Babes-Bolyai University, Romania

Diana Otrocol
Department of Mathematics, Technical University of Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy


Volterra integral equation with delay; w-distance; weakly Picard operator; abstract Gronwall lemma



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V. Ilea and D. Otrocol, On a Volterra integral equation with delay, via w-distances, Mathematics, 9 (2021), art. id. 2341. https://doi.org/10.3390/math9182341

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