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


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.


Veronica Ilea
Babeş-Bolyai University, Department of Mathematics, Cluj-Napoca, Romania

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


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


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.

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