On the Constants in Videnskiĭ Type Inequalities for Bernstein Operators
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DOI: 10.1007/s00025-017-0707-3
Abstract: This paper deals with the approximation of functions by Bernstein operators. Specifically, the interest is mainly focused on the constants in Videnskiĭ type inequalities, which turn out to be quantitative versions of the well known… read more here.
Keywords: bernstein operators; videnski type; inequalities bernstein; constants videnski ... See more keywords
RETRACTED ARTICLE: On eigenstructure of q-Bernstein operators
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DOI: 10.1007/s13324-020-00443-7
Abstract: The quantum analogue of Bernstein operators $${\mathcal {B}}_{m,q}$$ reproduce the linear polynomials which are therefore eigenfunctions corresponding to the eigenvalue $$1,~\forall ~ q>0$$ . In this article the rest of eigenstructure of q-Bernstein operators and… read more here.
Keywords: bernstein; eigenstructure bernstein; bernstein operators; retracted article ... See more keywords
On the monotonicity property for the sequence of classical Bernstein operators
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DOI: 10.1007/s13370-018-0602-4
Abstract: This note presents the proof of monotonicity property for the sequence of classical Bernstein operators, involving divided differences and convex functions. As application, we get the form of remainder term associated to the classical Bernstein… read more here.
Keywords: bernstein operators; monotonicity property; property sequence; classical bernstein ... See more keywords
Approximation of functions by a new family of generalized Bernstein operators
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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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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
On the convergence of Lupaş (p,q)$(p,q)$-Bernstein operators via contraction principle
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DOI: 10.1186/s13660-019-1985-y
Abstract: The present paper deals with the limit behavior of iterates of Lupaş q- and (p,q)$(p,q)$-Bernstein operators. We obtain the convergence for Lupaş q- and (p,q)$(p,q)$-Bernstein operators by using the contraction principle. read more here.
Keywords: contraction principle; bernstein operators; convergence lupa; lupa bernstein ... See more keywords
Convergence of iterates of q-Bernstein and (p,q)-Bernstein operators and the Kelisky-Rivlin type theorem
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DOI: 10.2298/fil1812351r
Abstract: Recently, Radu [Note on the iterates of q and (p, q)-Bernstein operators, Scientific Studies and Research, Series Mathematics and Informatics, 26(2) (2016) 83-94] has investigated the convergence of iterates of q-Bernstein polynomial and (p, q)-Bernstein… read more here.
Keywords: bernstein; convergence iterates; bernstein operators; rivlin type ... See more keywords
Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ
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DOI: 10.3390/sym11030316
Abstract: We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ - 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by… read more here.
Keywords: operators based; type bernstein; bernstein operators; stancu type ... See more keywords