On Durrmeyer type \(\lambda\)-Bernstein operators via \((p,q)\)-calculus (Q2220504)

The authors construct Durrmeyer type generalized Bernstein operators via $(p, q)$-calculus. The first and second moments and central moments of these operators are estimated and a Korovkin type approximation theorem is established. To estimate the rate of convergence, the modulus of continuity of second order and Steklov means are used. The paper contains also a convergence theorem for the Lipschitz continuous functions. Finally, some numerical examples are given to show that the new operators converge faster than Durrmeyer type $(p, q)$-Bernstein operators.