Abstract
We construct the blending-type modified Bernstein–Durrmeyer operators and investigate their approximation properties. First, we derive the Voronovskaya-type asymptotic theorem for this type of operator. Then, the local and global approximation theorems are obtained by using the classical modulus of continuity and K-functional. Finally, we derive the rate of convergence for functions with a derivative of bounded variation. The results show that the new operators have good approximation properties.
Funder
National Natural Science Foundation of China
Key Natural Science Research Project in Universities of Anhui Province
Philosophy and Social Sciences General Planning Project of Anhui Province of China
Natural Science Foundation of Anhui Province of China
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
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