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Numerical solvability of Hammerstein integral equations of mixed type. (English) Zbl 0719.65093

The authors consider integral equations of the form \((*)\quad x(s)+\sum^{m}_{i=1}\int^{b}_{a}k_ i(s,t)f_ i(t,x(t))dt=y(s),\quad s\in [a,b].\) The existence and uniqueness of a solution to (*) is proved and the numerical solvability of (*) by using a collocation type method is studied. Convergence and error estimates are given. A simple test example is considered.
[Remark: The definition of N in (2.4) must be replaced by \(N:=(N_ 1(x_ 1),N_ 2(x_ 2),...,N_ m(x_ m))^ T\). Furthermore, the considering of the problem in the product space \(\prod^{m}_{i=1}X\) is not necessary.]

MSC:

65R20 Numerical methods for integral equations
45G10 Other nonlinear integral equations
45N05 Abstract integral equations, integral equations in abstract spaces
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