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APPLICATIONS OF FIBRE CONTRACTION PRINCIPLE TO SOME CLASSES OF FUNCTIONAL INTEGRAL EQUATIONS.
- Source :
-
Fixed Point Theory . 2022, Vol. 23 Issue 1, p279-291. 13p. - Publication Year :
- 2022
-
Abstract
- Let a < c < b real numbers, (B, |·|) a (real or complex) Banach space, H ∈ C([a, b] x [a, c] x B,B), K ∈ C([a,b]² x 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) = ∫ac H(t,s,A(x)(s))ds + ∫at, 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15835022
- Volume :
- 23
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Fixed Point Theory
- Publication Type :
- Academic Journal
- Accession number :
- 155337463
- Full Text :
- https://doi.org/10.24193/fpt-ro.2022.1.18