DOI: 10.24193/fpt-ro.2024.2.10

Authors: Veronica Ilea and Diana Otrocol

Abstract: The aim of this paper is to emphasize the role of the fibre contraction principle in the study of the solution of integral equations with maxima in connection with the weakly Picard operator technique. The results complement and extend some known results given in the paper: I.A. Rus, Some variants of contraction principle in the case of operators with Volterra property: step by step contraction principle, Advances in the Theory of Nonlinear Analysis and its Applications, 3(2019), no. 3, 111-120. The last section is devoted to Gronwall lemma type results and comparison theorems.

Key Words and Phrases: Integral equation with maxima, existence and uniqueness, fixed point, weakly Picard operator, fibre contraction principle, Gronwall lemma, comparison lemma.

2010 Mathematics Subject Classification: 47H10, 47H09, 45J05.

Published on-line: June 15th, 2024.

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