Approximating the solution of nonlinear Hammerstein fuzzy integral equations

Numerical solution of two-dimensional nonlinear Hammerstein fuzzy integral equations based on optimal fuzzy quadrature formula

“…Applying the Banach fixed point principle we obtain the existence of the unique solution, F * ∈ C A, R ̥ , of (1) and the uniform convergence of the sequence of successive approximations (10) to this solution in C (A, R ̥ ), D * , for any choice of the initial term of F 0 ∈ C A, R ̥ .…”

“…For any partitions a ≤ ξ 1 < ... < ξ n ≤ b and c ≤ η 1 < η 2 < ... < η n ≤ d of intervals [a, b] and [c, d], respectively, let σ = (b − a)/n, σ ′ = (d − c)/n. we apply fuzzy quadrature formula (8) in the computation of the terms of the sequence of successive approximations (10).…”

“…The study of fuzzy integral equations begins with the investigations of Kaleva [20] and Seikkala [33] for fuzzy Volterra integral equations that is equivalent to the initial value problem for the first order fuzzy differential equations. This concept was developed by many researchers [8,10,19,34,35]. The Banach's fixed point theorem and method of successive approximations are applied in the problem of the existence and uniqueness of the solution, (see [6,7,15,16,26,27,28]).…”

“…The Banach's fixed point theorem and method of successive approximations are applied in the problem of the existence and uniqueness of the solution, (see [6,7,15,16,26,27,28]). In [10,25] authors presented sufficient conditions for bounded solutions of fuzzy integral equations. In [13] a numerical method to solve nonlinear fuzzy integral equations was proposed.…”

Numerical solution of nonlinear Urisohn-Volterra fuzzy functional integral equations

“…Then we study the existence and uniqueness of the solution of (1), the uniform boundedness and uniform Lipschitz properties of the sequence of successive approximations. Also we present the algorithm for approximating the solution of (1). In addition, the convergence of this algorithm and its numerical stability with respect to the choice of the first iteration are proved.…”