Abstract
We study statistical approximation properties of -Bernstein-Shurer operators and establish some direct theorems. Furthermore, we compute error estimation and show graphically the convergence for a function by operators and give its algorithm.
Highlights
Introduction and PreliminariesIn 1987, Lupas [1] introduced the first q-analogue of Bernstein operator and investigated its approximating and shapepreserving properties
Another q-generalization of the classical Bernstein polynomials is due to Phillips [2]
The statistical approximation properties have been investigated for q-analogue polynomials
Summary
In 1987, Lupas [1] introduced the first q-analogue of Bernstein operator and investigated its approximating and shapepreserving properties. Another q-generalization of the classical Bernstein polynomials is due to Phillips [2]. After that many generalizations of well-known positive linear operators, based on q-integers, were introduced and studied by several authors. The statistical approximation properties have been investigated for q-analogue polynomials. Muraru [13] introduced the q-analogue of these operators and investigated their approximation properties and rate of convergence using modulus of continuity. Note that Radu [14] has used q-intgers to define and study the approximation properties of the q-analogue of Kantorovich operators.
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