Ganesh, M.; Joshi, M. C. Numerical solvability of Hammerstein integral equations of mixed type. (English) Zbl 0719.65093 IMA J. Numer. Anal. 11, No. 1, 21-31 (1991). 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.] Reviewer: W.Petry (Düsseldorf) Cited in 55 Documents MSC: 65R20 Numerical methods for integral equations 45G10 Other nonlinear integral equations 45N05 Abstract integral equations, integral equations in abstract spaces Keywords:monotonicity methods; Leray-Schauder principle; collocation; Convergence; error estimates; test example PDFBibTeX XMLCite \textit{M. Ganesh} and \textit{M. C. Joshi}, IMA J. Numer. Anal. 11, No. 1, 21--31 (1991; Zbl 0719.65093) Full Text: DOI