A generalization of the Bernstein polynomials based on the q-integers

By George M. Phillips. The ANZIAM Journal, 2000

350 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e72b1f4299fa44f2d280dde2c2f2b9e737753596

How researchers see this paper

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In Computational Mechanics

1. Tuncer Acar
2. Vijay Gupta
3. Ali Aral
4. Taekyun Kim
5. Heping Wang
6. Ogün Dogru
7. Cristina Radu
8. Halil Oruç

In Numerical Analysis

1. Tuncer Acar
2. Vijay Gupta
3. Ali Aral
4. Cristina Radu
5. Gülsüm Ulusoy
6. Ogün Dogru
7. Taekyun Kim
8. Heping Wang

In Statistics and Probability

1. Tuncer Acar
2. Vijay Gupta
3. Gülsüm Ulusoy
4. Ali Aral
5. Ogün Dogru
6. Cristina Radu
7. Taekyun Kim
8. Halil Oruç

Citations in the corpus

• A note on q-Bernstein polynomials (2010, methodology): “In the reference [15] and [16], Phillips proposed a generalization of classical Bernstein polynomials based on q-integers.”
• Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers (2015, neutral): “In 1997, Phillips [11] introduced another modification of Bernstein polynomials.”
• Statistical approximation properties of q-Baskakov-Kantorovich operators (2009, methodology): “Phillips [17] proposed a generalization of the classical Bernstein polynomials based on q-integers.”
• On Pointwise Convergence of q-Bernstein Operators and Their q-Derivatives (2015, background): “Philips [16] introduced q -Bernstein polynomials for n ∈ and f ∈ C 0, 1 by”
• On the Lupaş $q$-Analogue of the Bernstein Operator (2006, background): “G.M. Phillips, Bernstein polynomials based on the q-integers, Annals Numer.”
• Generalized -Bernstein-Schurer Operators and Some Approximation Theorems (2013, neutral): “[2] G. M. Phillips, “Bernstein polynomials based on the q-integers, Theheritage of P.L. Chebyshev,”Annals of NumericalMathematics, vol. 4, pp. 511–518, 1997.”
• Some approximation results involving the q‐Szász–Mirakjan–Kantorovich type operators via Dunkl's generalization (2017, background): “Phillips GM. Bernstein polynomials based on the q-integers.”
• Properties of convergence for the q-Meyer-König and Zeller operators (2007, background): “In [9], Phillips proposed the q-Bernstein polynomials: for each positive integer n, and f ∈ C[0,1], the q-Bernstein polynomial of f is Bn,q(f, x) := n ∑ k=0 f ( [k] [n] )[ n k ] x(x;q)n−k.”
• Bleimann, Butzer, and Hahn Operators Based on the-Integers (2007, methodology): “Later, some results are established in due course by Phillips et al. (see [2, 3, 1]).”
• The rate of convergence of q‐Durrmeyer operators for 0 (2008, background): “Phillips GM. Interpolation and Approximation by Polynomials.”
• Generalized q-Baskakov operators (2011, background): “In 1997, Phillips [25] (see also [27]) introduced another generalization of Bernstein operators based on the q-integers called q-Bernstein operators.”
• Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators (2016, methodology): “After the construction of q-Bernstein polynomials in [18] and [21], various generalizations of the well-known Szász–Mirakyan operators in q-calculus were introduced.”
• q -Bernstein polynomials and Bézier curves (2003, methodology): “The q-Bernstein polynomials were defined as follows by the second author [15]:”
• q‐Voronovskaya type theorems for q‐Baskakov operators (2016, methodology): “In the paper [11], Philips introduced the generalization of Bernstein polynomials based on q-integers.”