A Special Type of Hammerstein Integral Equations.
ISSN: 0129-167X
Año de publicación: 2002
Volumen: 1
Páginas: 557-566
Tipo: Artículo
Otras publicaciones en: International Journal of Mathematics
Resumen
The authors analyze the convergence of Newton's iteration method for the solution of the nonlinear second-kind integral equation of Hammerstein typex(s)=h(s)+λ∫baG(s,t)x(t)1+pdt,s∈[a,b],where h>0 and G≥0 are continuous, p∈[0,1] and λ is real. Employing a modification of the classical Newton-Kantorovich theorem, they prove the convergence of Newton's method and the uniqueness of the solution in a neighborhood of the starting function.