On some midpoint-type algorithms.

Abstract

We introduce iterative methods approximating fixed points for nonlinear operators defined on infinite-dimensional spaces. The starting points are the Implicit and Explicit Midpoint Rules, which generate polygonal functions approximating a solution for an ordinary differential equation infinite-dimensional spaces. The purpose is to determine suitable conditions on the mapping and the underlying space, in order to get strong convergence of the generated sequence to a common solution of a fixed point problem and a variational inequality.