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Statistical approximation properties of the Durrmeyer type q ‐Bleimann, Butzer, and Hahn operators
Author(s) -
Cai QingBo,
Zeng XiaoMing
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1520
Subject(s) - mathematics , modulus of continuity , type (biology) , generalization , lipschitz continuity , pure mathematics , mathematical analysis , discrete mathematics , ecology , biology
In this paper, we introduce a Durrmeyer‐type generalization of q ‐Bleimann, Butzer, and Hahn operators based on q ‐integers and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. We also compute rates of statistical convergence of these q ‐type operators by means of the modulus of continuity and Lipschitz‐type maximal function, respectively. Copyright © 2011 John Wiley & Sons, Ltd.
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