## 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.

## Authors

**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

## Keywords

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

## References

##### Cite this paper as:

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

## About this paper

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##### Online ISSN

**2227-7390**

##### Google Scholar Profile

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