The Numerical Evaluation of Fixed Points for Completely Continuous Operators

Given a completely continuous nonlinear operator K on a domain D contained in a Banach space X, one common way of approximating K leads to a sequence \ Kₙ \ which is collectively compact and pointwise convergent to K on D. If K is an integral operator, then Kₙ would usually be the result of replacing the integral with a numerical integral which depended on n. The results given here concern local existence and uniqueness of fixed points of Kₙ and convergence of them to fixed points of K. The approach used is the invariance under homotopy of the rotation of a completely continuous vector field.