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[en] 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 normed linear spaces. We use them to obtain new stability evaluations for continuous selectors of the operator P
Journal
Izvestiya. Mathematics; ISSN 1064-5632; 
; v. 62(2); p. 313-318
; v. 62(2); p. 313-318