1. APPLICATIONS OF FIBRE CONTRACTION PRINCIPLE TO SOME CLASSES OF FUNCTIONAL INTEGRAL EQUATIONS.
- Author
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ILEA, VERONICA, OTROCOL, DIANA, RUS, IOAN A., and ŞŞERBAN, MARCEL-ADRIAN
- Subjects
FUNCTIONAL equations ,INTEGRAL equations ,BANACH spaces ,VOLTERRA operators ,REAL numbers - 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) = ∫
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. [ABSTRACT FROM AUTHOR]- Published
- 2022
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