Existence and uniqueness of the solution for an integral equation with supremum

Abstract

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

Authors

Veronica Ilea
Babeş–Bolyai University, Department of Mathematics, 1 M. Kogălniceanu Street, 400084 Cluj-Napoca, Romania

Diana Otrocol
Technical University of Cluj-Napoca, Department of Mathematics, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, P.O. Box 68-1, 400110 Cluj-Napoca, Romania

Keywords

w-distance; integral equation with supremum; abstract Gronwall theorem; weakly Picard operator; Ulam-Hyers stability;

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Cite this paper as:

V. Ilea, D. Otrocol, Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances, Symmetry 2020, 12, 1554,
symmetry-12-01554-v2.pdf

About this paper

Journal

Symmetry

Publisher Name

MDPI

Print ISSN

2073-8994

Online ISSN

Not available yet.

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References

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