On best-approximation problems for nonlinear operators (Q2778297)

The authors present a comparative study of recent methods in the best approximation of nonlinear operators and provide then new results in this area. The paper is organized as follows. In Section 2 the best approximation in deterministic spaces is considered, whereby a generic representation of the best approximating operator is presented, as well as theorems which establish its approximating properties. In Section 3 two approaches for the best approximation of nonlinear operators acting in probability spaces are proposed. The first is based upon the quadratic structure of the approximating operator, and the second approach employs a combination of a special iterative procedure and the specific best quadratic solution on each iteration loop.