ON THE RATE OF CONVERGENCE OF THE GENERALIZED SZASZ TYPE OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

Authors
ZENG XM
Citation
Xm. Zeng, ON THE RATE OF CONVERGENCE OF THE GENERALIZED SZASZ TYPE OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION, Journal of mathematical analysis and applications (Print), 226(2), 1998, pp. 309-325
Citations number
10
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
Journal title
Journal of mathematical analysis and applications (Print) → ACNP
ISSN journal
0022247X
Volume
226
Issue
2
Year of publication
1998
Pages
309 - 325
Database
ISI
SICI code
0022-247X(1998)226:2<309:OTROCO>2.0.ZU;2-E
Abstract
In this article we introduce the Szasz-Bezier operator S-n,S- alpha wh ich is the modified form of the Szasz-Mirakyan operator. By means of c onstruction of suitable functions and the methods of Bojanic-Vuillemie r [J. Approx. Theory 31 (1981), 67-79] and Cheng [J. Approx. Theory 40 (1984), 226-241], using some results and techniques of probability th eory, we obtain the rate of convergence of S-n,S- alpha for functions of bounded variation. Our results extend and sharpen the results of Ch eng [J. Approx. Theory 40 (1984), 226-241], Guo and Khan [J. Approx. T heory 58 (1989), 90-101] for the Szasz-Mirakyan operator. (C) 1998 Aca demic Press.