scholarly journals Rate of convergence for the Bézier variant of the Bleimann–Butzer–Hahn operators

2005 ◽  
Vol 18 (8) ◽  
pp. 849-857 ◽  
Author(s):  
H.M. Srivastava ◽  
Vijay Gupta
Keyword(s):  
Rate Of Convergence ◽  
Bézier Variant

scholarly journals Bézier variant of the Szász-Durrmeyer type operators based on the Poisson-Charlier polynomials

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3265-3273
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Charlier Polynomials ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In the present paper we introduce the B?zier variant of the Sz?sz-Durrmeyer type operators, involving the Poisson-Charlier polynomials. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness and the rate of convergence for differential functions whose derivatives are of bounded variation.

Rate of convergence of the Bézier variant of an operator involving Laguerre polynomials

2016 ◽  
Vol 41 (3) ◽  
pp. 912-919 ◽  
Author(s):  
Özlem Öksüzer ◽  
Harun Karsli ◽  
Fatma Taşdelen Yeşildal
Keyword(s):  
Rate Of Convergence ◽  
Laguerre Polynomials ◽  
Bézier Variant

scholarly journals Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lahsen Aharouch ◽  
Khursheed J. Ansari ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Modulus Of Smoothness ◽  
Weighted Modulus Of Continuity ◽  
Type Formula ◽  
Weighted Modulus ◽  
Bézier Variant

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

scholarly journals Approximation of bounded variation functions by a Bézier variant of the Bleimann, Butzer, and Hahn operators

2006 ◽  
Vol 2006 ◽  
pp. 1-5 ◽  
Author(s):  
Vijay Gupta ◽  
Ogün Doğru
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Sharp Estimate ◽  
Functions Of Bounded Variation ◽  
Bounded Variation Functions ◽  
Bézier Variant

We give a sharp estimate on the rate of convergence for the Bézier variant of Bleimann, Butzer, and Hahn operators for functions of bounded variation. We consider the case whenα≥1and our result improves the recently established results of Srivastava and Gupta (2005) and de la Cal and Gupta (2005).

scholarly journals Rate of approximation for the Bézier variant of Balazs Kantorovich operators

2007 ◽  
Vol 57 (4) ◽  
Author(s):  
Vijay Gupta ◽  
X. Zeng
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Rate Of Approximation ◽  
Kantorovich Operators ◽  
Bézier Variant

AbstractIn the present paper we study the Bézier variant of the well known Balazs-Kantorovich operators L n,α(f,x), α ≥ 1. We establish the rate of convergence for functions of bounded variation. For particular value α = 1, our main theorem completes a result due to Agratini [Math. Notes (Miskolc) 2 (2001), 3–10].

Bézier variant of Bernstein–Durrmeyer blending-type operators

2021 ◽  
pp. 2250103
Author(s):  
Chandra Prakash ◽  
Naokant Deo ◽  
D. K. Verma
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Graphical Representation ◽  
Type Function ◽  
Rate Of Approximation ◽  
Durrmeyer Type Operators ◽  
Derivatives Of ◽  
Theoretical Results ◽  
Bézier Variant

In this paper, we construct the Bézier variant of the Bernstein–Durrmeyer-type operators. First, we estimated the moments for these operators. In the next section, we found the rate of approximation of operators [Formula: see text] using the Lipschitz-type function and in terms of Ditzian–Totik modulus of continuity. The rate of convergence for functions having derivatives of bounded variation is discussed. Finally, the graphical representation of the theoretical results and the effectiveness of the defined operators are given.

scholarly journals Rate of convergence on Baskakov-Beta-Bezier operators for bounded variation functions

2002 ◽  
Vol 32 (8) ◽  
pp. 471-479 ◽  
Author(s):  
Vijay Gupta
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Open Problem ◽  
Positive Operators ◽  
Functions Of Bounded Variation ◽  
Linear Positive Operators ◽  
Bounded Variation Functions ◽  
Bézier Variant

We introduce a new sequence of linear positive operatorsBn,α(f,x), which is the Bezier variant of the well-known Baskakov Beta operators and estimate the rate of convergence ofBn,α(f,x)for functions of bounded variation. We also propose an open problem for the readers.

scholarly journals Rate of Convergence for the Bézier Variant of the MKZD Operators

2007 ◽  
Vol 14 (4) ◽  
pp. 651-659
Author(s):  
Vijay Gupta ◽  
Harun Karsli
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Derivatives Of ◽  
Bézier Variant

Abstract We estimate the rate of convergence of the Bézier variant of Durrmeyer type Meyer–König and Zeller operators for functions with derivatives of bounded variation defined on [0, 1].

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