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Existence of solutions of fuzzy integral equations in Banach spaces. (English) Zbl 0844.45010
We consider the fuzzy integral equation $$\varphi (u) = w_0 + \int^u_{u_0} F \bigl( u,s, \varphi (s) \bigr) ds, \quad \varphi(u_0) = w_0, \tag 1$$ where $F : J \times J \times T(X) \to T(X)$ is continuous, $J = [u_0, u_0 + d]$, and $T(X)$ is a regular fuzzy set. The purpose of this paper is to study the local existence of solutions and the approximate solutions for problem (1), based on the properties of the $\alpha$-index of Kuratowski.

45N05Abstract integral equations, integral equations in abstract spaces
45G10Nonsingular nonlinear integral equations
03E72Fuzzy set theory
47H09Mappings defined by “shrinking” properties
Full Text: DOI
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