On Durrmeyer Type$\lambda$-Bernstein Operators via ($p$,$q$)-Calculus

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.