Posts by Diana Otrocol

Abstract

Let a<c<b real numbers, (B,|·|) a (real or complex) Banach space, H∈C([a,b]×[a,c]×B,B),K∈C([a,b]² ×B,B),g∈C([a,b],B),A:C([a,c],B)→C([a, c], B) and B:C([a,b],B)→C([a,b],B). In this paper we study the following functional integral equation,

x(t)=∫_{a}^{c}H(t,s,A(x)(s))ds+∫_{a}^{t}K(t,s,B(x)(s))ds+g(t),t∈[a,b]. By a new variant of fibre contraction principle (A. Petrusel, I.A. Rus, M.A. Serban, Some variants of fibre contraction principle and applications: from existence to the convergence of successive approximations, Fixed Point Theory, 22 (2021), no. 2, 795-808) we give existence, uniqueness and convergence of successive approximations results for this equation. In the case of ordered Banach space B, Gronwall-type and comparison-type results are also given.

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,
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

Ioan A. Rus
Babes-Bolyai University, Faculty of Mathematics and Computer Science,Cluj-Napoca, Romania

Marcel-Adrian Serban
Babes-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania

Keywords

Functional integral equation, Volterra operator, Picard operator, fibre contraction principle, Gronwall lemma, comparison lemma.

Paper coordinates

V. Ilea, D. Otrocol, I.A. Rus, M.-A. Serban, Applications of fibre contraction principle to some classes of functional integral equations, Fixed Point Theory, 23 (2022) no. 1, 279-292, http://doi.org/10.24193/fpt-ro.2022.1.18

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About this paper

Journal

Fixed Point Theory

Publisher Name

Casa Cărţii de Ştiinţă Cluj-Napoca
(House of the Book of Science Cluj-Napoca)

DOI

http://doi.org/10.0.94.129/fpt-ro.2022.1.18

Print ISSN

1583-5022

Online ISSN

2066-9208

google scholar link

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