On a Fredholm-Volterra integral equation
DOI:
https://doi.org/10.24193/subbmath.2021.3.12Keywords:
Fredholm-Volterra integral equation, existence, uniqueness, contraction, fiber contraction, Maia theorem, successive approximation, fixed point, Picard operator.Abstract
In this paper we give conditions in which the integral equation
x(t) =r c K(t, s, x(s))ds + a r t H(t, s, x(s))ds + g(t), t ∈ [a, b], a
where a < c < b, K ∈ C([a, b] × [a, c] × B, B), H ∈ C([a, b] × [a, b] × B, B), g ∈ C([a, b], B), with B a (real or complex) Banach space, has a unique solution in C([a, b], B). An iterative algorithm for this equation is also given.
Mathematics Subject Classification (2010): 45N05, 47H10, 47H09, 54H25.
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