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Generalized Bernstein‐Kantorovich–type operators on a triangle

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0 Published in 2019 at "Mathematical Methods in the Applied Sciences"

DOI: 10.1002/mma.5656

Abstract: In this note, we construct generalized Bernstein‐Kantorovich–type operators on a triangle. The concern of this note is to present a Voronovskaja‐type and Grüss Voronovskaja‐type asymptotic theorems, and some estimates of the rate of approximation with… read more here.

Keywords: kantorovich type; bernstein kantorovich; generalized bernstein; type operators ... See more keywords

Blending Type Approximation by GBS Operators of Generalized Bernstein–Durrmeyer Type

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1 Published in 2018 at "Results in Mathematics"

DOI: 10.1007/s00025-018-0773-1

Abstract: In this article we study an extension of the bivariate generalized Bernstein–Durrmeyer operators based on a non-negative real parameter. For these operators we get a Voronovskaja type theorem, the order of approximation using Peetre’s K-functional… read more here.

Keywords: operators generalized; durrmeyer type; approximation; generalized bernstein ... See more keywords

Approximation of functions by a new family of generalized Bernstein operators

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0 Published in 2017 at "Journal of Mathematical Analysis and Applications"

DOI: 10.1016/j.jmaa.2016.12.075

Abstract: Abstract The main object of this paper is to construct a new generalization of the Bernstein operator, depending on a non-negative real parameter. We investigate some elementary properties of this operator, such as end point… read more here.

Keywords: bernstein; bernstein operators; generalized bernstein; approximation functions ... See more keywords

Shape-preserving properties of a new family of generalized Bernstein operators

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0 Published in 2018 at "Journal of Inequalities and Applications"

DOI: 10.1186/s13660-018-1821-9

Abstract: In this paper, we introduce a new family of generalized Bernstein operators based on q integers, called (α,q)$(\alpha,q)$-Bernstein operators, denoted by Tn,q,α(f)$T_{n,q,\alpha}(f)$. We investigate a Kovovkin-type approximation theorem, and obtain the rate of convergence of… read more here.

Keywords: bernstein operators; generalized bernstein; family generalized; new family ... See more keywords

Blending type approximation by generalized Bernstein-Durrmeyer type operators

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0 Published in 2018 at "Miskolc Mathematical Notes"

DOI: 10.18514/mmn.2018.2216

Abstract: The approximation theory by linear positive operators investigates how the functions can be best approximated by simpler functions. The most famous basic result for convergence of linear positive operators is due to Weierstrass who introduced… read more here.

Keywords: approximation; generalized bernstein; approximation generalized; type ... See more keywords