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.

On the rate of convergence of some integral operators for functions of bounded variation

2005 ◽  
Vol 42 (2) ◽  
pp. 235-252
Author(s):  
Octavian Agratini
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
General Class ◽  
Pointwise Convergence ◽  
Integral Operators ◽  
Positive Operators ◽  
Functions Of Bounded Variation ◽  
Linear Positive Operators ◽  
The One

In the present paper we define a general class Bn,a, a =1, of Durrmeyer-Bézier type of linear positive operators. Our main aim is to estimate the rate of pointwise convergence for functions f at those points x at which the one-sided limits f(x+) and f(x-) exist. As regards these functions defined on an interval J certain conditions are required. We discuss two distinct cases: Int (J)=(0,8) and Int (J)=(0,1).

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 A note on integral modification of the Meyer-König and Zeller operators

2003 ◽  
Vol 2003 (31) ◽  
pp. 2003-2009 ◽  
Author(s):  
Vijay Gupta ◽  
Niraj Kumar
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Present Note ◽  
Sharp Estimate ◽  
Functions Of Bounded Variation ◽  
Exact Bound ◽  
Bounded Variation Functions ◽  
Correct Estimate

Guo (1988) introduced the integral modification of Meyer-Kö nig and Zeller operatorsMˆnand studied the rate of convergence for functions of bounded variation. Gupta (1995) gave the sharp estimate for the operatorsMˆn. Zeng (1998) gave the exact bound and claimed to improve the results of Guo and Gupta, but there is a major mistake in the paper of Zeng. In the present note, we give the correct estimate for the rate of convergence on bounded variation functions.

scholarly journals Rate of convergence of bounded variation functions by a Bézier-Durrmeyer variant of the Baskakov operators

2004 ◽  
Vol 2004 (9) ◽  
pp. 459-468 ◽  
Author(s):  
Vijay Gupta ◽  
Ulrich Abel
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Baskakov Operators ◽  
Bounded Variation Functions ◽  
Durrmeyer Variant

We consider a Bézier-Durrmeyer integral variant of the Baskakov operators and study the rate of convergence for functions of bounded variation.

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].

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

Sign in / Sign up

Export Citation Format

Share Document