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Integral equation with maxima via fibre contraction principle

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.

Authors

Veronica Ilea
Babes-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania

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

Keywords

comparison lemma; existence and uniqueness; fibre contraction principle; fixed point; Gronwall lemma; Integral equation with maxima; weakly Picard operator

Paper coordinates

V. Ilea, D. Otrocol, Integral equation with maxima via fibre contraction principle, Journal Fixed Point Theory, 25 (2024) 2, pp. 601-610, http://doi.org/10.24193/fpt-ro.2024.2.10

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About this paper

Journal

Fixed Point Theory

Publisher Name

House of the Book of Science Cluj-Napoca

Print ISSN

1583-5022

Online ISSN

2066-9208

google scholar link

2024

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