2015•arXiv (Cornell University)Open access

On (p,q)-analogue of Bernstein Operators

M. Mursaleen, Khursheed J‎. ‎Ansari, Asif Khan

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Abstract

In this paper, we introduce a new analogue of Bernstein operators and we call it as (p, q)-Bernstein operators which is a generalization of q-Bernstein operators. We also study approximation properties based on Korovkin’s type approximation theorem of (p, q)-Bernstein operators and establish some direct theorems. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.

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What this paper is about

In this paper, we introduce a new analogue of Bernstein operators and we call it as (p, q)-Bernstein operators which is a generalization of q-Bernstein operators. We also study approximation properties based on Korovkin’s type approximation theorem of (p, q)-Bernstein operators and establish some direct theorems. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.

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Available abstract

In this paper, we introduce a new analogue of Bernstein operators and we call it as (p, q)-Bernstein operators which is a generalization of q-Bernstein operators. We also study approximation properties based on Korovkin’s type approximation theorem of (p, q)-Bernstein operators and establish some direct theorems. Furthermore, we show comparisons and some illustrative graphics for the convergence of operators to a function.

Key concepts: Bernstein polynomial, Operator theory, Baskakov operator, Generalization, Spectral theorem, Convergence (economics), Mathematics, Type (biology)

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