On some midpoint-type algorithms.

Abstract

We introduce iterative methods approximating fixed points for nonlinear operators defined on infinitedimensional spaces. The starting points are the Implicit and Explicit Midpoint Rules, which generate polygonal functions approximating a solution for an ordinary differential equation in finite-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. The authors contributions appear in the papers [34], [60], [61].