Statistical Approximation of the q-Bernstein-Durrmeyer Type Operators

  • Mei-Ying Ren
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)


In 2012, a kind of q-Bernstein-Durrmeyer type operators is introduced, and some approximate properties of these operators are studied by Ren. In this paper the statistical approximation properties of these operators are investigated. The Korovkin type statistical convergence theorem of these operators is established. Then the rates of statistical convergence of these operators are also studied by means of modulus of continuity and the help of functions of the Lipschitz class.


q-Bernstein-Durrmeyer type operators q-integers Korovkin type theorem Rate of statistical convergence Modulus of continuity 



This work is supported by the National Natural Science Foundation of China (No. 61170324), the Class A Science and Technology Project of Education Department of Fujian Province of China (No. JA12324), and the Natural Science Foundation of Fujian Province of China (No. 2013J01017 and No. 2014J01021).


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceWuyi UniversityWuyishanChina

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