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

Author

Listed:
  • 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
    Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania)

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.

Suggested Citation

  • Veronica Ilea & Diana Otrocol, 2021. "On a Volterra Integral Equation with Delay, via w -Distances," Mathematics, MDPI, vol. 9(18), pages 1-8, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2341-:d:639727
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