Local approximation by a variant of Bernstein-Durrmeyer operators
Abbreviated Journal Title
Nonlinear Anal.-Theory Methods Appl.
approximation by positive operators; rate of convergence; degree of; approximation; functions of bounded variation; total variation; sharp; bound; asymptotic expansions; MEYER-KONIG; ASYMPTOTIC APPROXIMATION; ZELLER OPERATORS; BLEIMANN; BUTZER; HAHN; Mathematics, Applied; Mathematics
This paper deals with the local approximation properties of a certain variant (M) over tilden of the Bernstein-Durrmeyer operators. Firstly, we obtain an estimate on the rate of convergence of (M) over tilden by means of the decomposition technique for functions of bounded variation. It will be shown that our estimate in its most convenient form (Corllary 2) is asymptotically optimal. Furthermore, we derive the complete asymptotic expansion for the sequence of the operators (M) over tilden as n tends to infinity. (C) 2007 Elsevier Ltd. All rights reserved.
Nonlinear Analysis-Theory Methods & Applications
"Local approximation by a variant of Bernstein-Durrmeyer operators" (2008). Faculty Bibliography 2000s. 45.