Open AccessOn Durrmeyer Type-Bernstein Operators via (,)-Calculus
Author(s) -
Qing-Bo Cai,
Guorong Zhou
Publication year - 2020
Publication title -
journal of function spaces
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.579
H-Index - 28
eISSN - 2314-8896
pISSN - 2314-8888
DOI - 10.1155/2020/8832627
Subject(s) - type (biology) , mathematics , convergence (economics) , algebra over a field , discrete mathematics , pure mathematics , ecology , economics , biology , economic growth
In the present paper, Durrmeyer type λ -Bernstein operators via ( p , q )-calculus are constructed, the first and second moments and central moments of these operators are estimated, a Korovkin type approximation theorem is established, and the estimates on the rate of convergence by using the modulus of continuity of second order and Steklov mean are studied, a convergence theorem for the Lipschitz continuous functions is also obtained. Finally, some numerical examples are given to show that these operators we defined converge faster in some λ cases than Durrmeyer type ( p , q )-Bernstein operators.