Approximation by Bézier variant of the Szász–Kantorovich operators in case α < 1

2010 ◽  
Vol 17 (2) ◽  
pp. 253-260
Author(s):  
Vijay Gupta ◽  
Xiao-Ming Zeng
Keyword(s):  
Bounded Variation ◽  
Convergence Theorem ◽  
Functions Of Bounded Variation ◽  
Approximation Properties ◽  
Approximation Of Functions ◽  
Type Approximation ◽  
Bounded Functions ◽  
Kantorovich Operators ◽  
Special Case ◽  
Bézier Variant

Abstract The present paper deals with the Bézier variant of the Szász–Kantorovich operator. Its approximation properties are studied. A convergence theorem of this type approximation operators for locally bounded functions is established, which subsumes the approximation of functions of bounded variation as a special case.

scholarly journals Approximation Properties of a Certain Modification of  Durrmeyer Operators

2021 ◽  
Author(s):  
Asha Ram Gairola ◽  
Karunesh Kumar Singh ◽  
Hassan Khosravian Arab ◽  
Vishnu Narayan Mishra
Keyword(s):  
Error Estimate ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Approximation Properties ◽  
Numerical Examples ◽  
Durrmeyer Operators ◽  
Integrable Functions ◽  
Durrmeyer Operator ◽  
Bézier Variant

Abstract We study approximation properties of a new operator DM,1 n (f, x) introduced by Acu et al. in [Results Math 74:90, (2019)] for Lebesgue integrable functions in [0,1]. An error estimate by the Bezier variant of the operators DM,1 n (f, x)is also obtained for the functions of bounded variation. By relevant numerical examples, the orders of approximation by the operator DM,1 n (f, x) and the modified-Bernstein-Durrmeyer operator are also compared.

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].

Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type

2012 ◽  
Vol 49 (2) ◽  
pp. 254-268
Author(s):  
Tiberiu Trif
Keyword(s):  
Rate Of Convergence ◽  
Finite Type ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Durrmeyer Operators

I. Gavrea and T. Trif [Rend. Circ. Mat. Palermo (2) Suppl. 76 (2005), 375–394] introduced a class of Meyer-König-Zeller-Durrmeyer operators “of finite type” and investigated the rate of convergence of these operators for continuous functions. In the present paper we study the approximation of functions of bounded variation by means of these operators.

A sharp trace inequality for functions of bounded variation in the ball

2012 ◽  
Vol 142 (6) ◽  
pp. 1179-1191 ◽  
Author(s):  
Andrea Cianchi
Keyword(s):  
Bounded Variation ◽  
Mean Value ◽  
Functions Of Bounded Variation ◽  
Trace Inequality ◽  
Best Constant ◽  
Isoperimetric Constant ◽  
Special Case

The best constant in a mean-value trace inequality for functions of bounded variation on admissible domains Ω ⊂ ℝn is shown to agree with an isoperimetric constant associated with Ω. The existence and form of extremals is also discussed. This result is exploited to compute the best constant in the relevant trace inequality when Ω is a ball. The existence and the form of extremals in this special case turn out to depend on the dimension n. In particular, the best constant is not achieved when Ω is a disc in ℝ2.

scholarly journals Weighted statistical approximation properties of univariate and bivariate λ-Kantorovich operators

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3473-3486 ◽  
Author(s):  
Faruk Özger
Keyword(s):  
Statistical Convergence ◽  
Approximation Theorem ◽  
Linear Operators ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Approximation ◽  
Bivariate Case ◽  
Estimate Rate ◽  
Kantorovich Operators

In this study, we consider statistical approximation properties of univariate and bivariate ?-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskajatype approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of ?-Bernstein and ?-Durrmeyer, and ?-Bernstein and ?-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case.

scholarly journals Rate of approximation of functions of bounded variation by modified Lupas operators

1991 ◽  
Vol 44 (2) ◽  
pp. 177-188 ◽  
Author(s):  
Wang Yuankwei ◽  
Guo Shunsheng
Keyword(s):  
Bounded Variation ◽  
Approximation Theorem ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Rate Of Approximation ◽  
Lupaş Operators

This paper discusses the rate of approximation of functions of bounded variation using the Modified Lupas operator. We obtain an approximation theorem and our estimate is essentially the best possible.

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 GENERALIZED BERNSTEIN-KANTOROVICH OPERATORS OF BLENDING TYPE

2019 ◽  
pp. 491
Author(s):  
Arun Kajla
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Approximation Properties ◽  
Mathematica Software ◽  
Kantorovich Operators ◽  
Appl Math

In this note, we derive some approximation properties of the generalized Bernstein-Kantorovich type operators based on two nonnegative parameters considered  by A. Kajla [Appl. Math. Comput. 2018]. We establish Voronovskaja type asymptotic theorem for these operators. The rate of convergence for differential functions whose derivatives are of bounded variation is also derived. Finally, we show the convergence of the operators by illustrative graphics in Mathematica software to certain functions.

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.

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