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
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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