Local smoothness of functions and Bernstein-Durrmeyer operators

Continuous functions satisfying a local Lipschitz condition of order #alpha#(0 < #alpha# < 1) on any subset of [0,1] are characterized by the local rate of convergence of Bernstein-Durrmeyer operators. As an application we give an algorithm for singular detection. A new direct estimate for the approximation of continuous functions by Bernstein-Durrmeyer operators and Kantorovich operators is also presented. (orig.)Available from TIB Hannover: RO 1945(291) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman