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 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 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 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.

DEFINITION AND CLASSIFICATION OF ONE-DIMENSIONAL CONTINUOUS FUNCTIONS WITH UNBOUNDED VARIATION

Fractals ◽  
2017 ◽  
Vol 25 (05) ◽  
pp. 1750048 ◽  
Author(s):  
Y. S. LIANG
Keyword(s):  
Fractal Dimension ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
One Dimensional ◽  
Nondifferentiable Functions ◽  
Differentiable Functions ◽  
Closed Intervals ◽  
Bounded Variation Functions

The present paper mainly investigates the definition and classification of one-dimensional continuous functions on closed intervals. Continuous functions can be classified as differentiable functions and nondifferentiable functions. All differentiable functions are of bounded variation. Nondifferentiable functions are composed of bounded variation functions and unbounded variation functions. Fractal dimension of all bounded variation continuous functions is 1. One-dimensional unbounded variation continuous functions may have finite unbounded variation points or infinite unbounded variation points. Number of unbounded variation points of one-dimensional unbounded variation continuous functions maybe infinite and countable or uncountable. Certain examples of different one-dimensional continuous functions have been given in this paper. Thus, one-dimensional continuous functions are composed of differentiable functions, nondifferentiable continuous functions of bounded variation, continuous functions with finite unbounded variation points, continuous functions with infinite but countable unbounded variation points and continuous functions with uncountable unbounded variation points. In the end of the paper, we give an example of one-dimensional continuous function which is of unbounded variation everywhere.

Sign in / Sign up

Export Citation Format

Share Document