On Durrmeyer Type λ-Bernstein Operators via (p, q)-Calculus. (27th November 2020) - Cai, Qing-Bo; Zhou, Guorong
Abstract : 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.