The Lipschitz constants of the metric ε-projection operator in spaces with given modules of convexity and smoothness

摘要

We obtain upper estimates for the Lipschitz constants of the metric ε-projection operator P in terms of the modules of convexity and smoothness of the space when the following three parameters are varied: the approximee x, the convex approximating set M, and the accuracy of approximation ε > 0. These estimates are unimprovable in the class of all normal linear spaces. We use them to obtain new stability evaluations for continuous selectors of the operator P.