Convergence of λ-Bernstein operators based on (p, q)-integers

Abstract

In the present paper, we construct a new class of positive linear λ-Bernstein operators based on (p, q)-integers. We obtain a Korovkin type approximation theorem, study the rate of convergence of these operators by using the conception of K-functional and moduli of continuity, and also give a convergence theorem for the Lipschitz continuous functions. MSC: 41A10; 41A25; 41A36

A-Statistical Convergence Properties of Kantorovich Type λ-Bernstein Operators Via (p, q)-Calculus

“…Proof. We get Equation (9) easily by Equations (5) and (6) and [23]. From Equations (5), (7), (8) and…”

“…Therefore, Equations (11) and (12) can be obtained by Equations (12), (14), [23] and some tedious computations, here we omit those processes.…”

“…Then, there are many papers mention about the approximation properties of (p, q)-type positive linear operators, such as . Very recently, Cai et al [23] proposed the following positive linear λ-Bernstein operators based on (p, q)-integers as…”

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