## 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

*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

## 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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