Convergence and Voronovskaja-type theorems for derivatives of generalized Baskakov operators

Abdul Wafi; Salma Khatoon

Open Mathematics (2008)

  • Volume: 6, Issue: 2, page 325-334
  • ISSN: 2391-5455

Abstract

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In the present paper our aim is to establish convergence and Voronovskaja-type theorems for first derivatives of generalized Baskakov operators for functions of one and two variables in exponential and polynomial weight spaces.

How to cite

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Abdul Wafi, and Salma Khatoon. "Convergence and Voronovskaja-type theorems for derivatives of generalized Baskakov operators." Open Mathematics 6.2 (2008): 325-334. <http://eudml.org/doc/269559>.

@article{AbdulWafi2008,
abstract = {In the present paper our aim is to establish convergence and Voronovskaja-type theorems for first derivatives of generalized Baskakov operators for functions of one and two variables in exponential and polynomial weight spaces.},
author = {Abdul Wafi, Salma Khatoon},
journal = {Open Mathematics},
keywords = {exponential weight spaces; derivatives of linear positive operators; convergence and Voronovskaja-type theorems; generalized Baskakov operators; Voronovskaja-type theorems},
language = {eng},
number = {2},
pages = {325-334},
title = {Convergence and Voronovskaja-type theorems for derivatives of generalized Baskakov operators},
url = {http://eudml.org/doc/269559},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Abdul Wafi
AU - Salma Khatoon
TI - Convergence and Voronovskaja-type theorems for derivatives of generalized Baskakov operators
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 325
EP - 334
AB - In the present paper our aim is to establish convergence and Voronovskaja-type theorems for first derivatives of generalized Baskakov operators for functions of one and two variables in exponential and polynomial weight spaces.
LA - eng
KW - exponential weight spaces; derivatives of linear positive operators; convergence and Voronovskaja-type theorems; generalized Baskakov operators; Voronovskaja-type theorems
UR - http://eudml.org/doc/269559
ER -

References

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  1. [1] Becker M., Global Approximation theorems for Szász-Mirkjan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J., 1978, 27, 127–142. http://dx.doi.org/10.1512/iumj.1978.27.27011 Zbl0358.41006
  2. [2] Becker M., Kucharski D., Nessel R.J., Global approximation theorems for the Szász-Mirkjan operators in exponential weight spaces, Linear Spaces and Approximation, Birkhäuser Verlag, Basel, ISNM, 1978, 40, 319–333 Zbl0386.41014
  3. [3] Firlej B., Rempulska L., Approximation of functions by some operators of the Szasz-Mirkjan-type, Fasc. Math., 1997, 27, 15–27. Zbl0898.41017
  4. [4] Gurdek M., Rempulska L., Skorupka M., The Baskakov operators for functions of two variables, Collect. Math., 1999, 50, 289–302 Zbl0955.41018
  5. [5] Mihesan V., Uniform approximation with positive linear operators generated by generalized Baskakov method, Automat. Comput. Appl. Math., 1998, 7, 34–37 
  6. [6] Rempulska L., Skorupka M., On the convergence of first derivatives of certain Szasz-Mirakyan type operators, Rend. Mat. Appl. (7), 1999, 19, 269–279 Zbl0960.41017
  7. [7] Skorupka M., Approximation of functions of two variables by some linear positive operators, Matematiche (Catania), 1995, 50, 323–336 Zbl0901.41018
  8. [8] Wafi A., Khatoon S., On the order of approximation of functions by generalized Baskakov operators, Indian J. Pure Appl. Math., 2004, 35, 347–358 Zbl1065.41044
  9. [9] Wafi A., Khatoon S., Approximation by generalized Baskakov operators for functions of one and two variables in exponential and polynomial weight spaces, Thai J. Math., 2004, 2, 53–66 Zbl1070.41013
  10. [10] Wafi A., Khatoon S., Direct and inverse theorems for generalized Baskakov operators in polynomial weight spaces, An. Ştiinţ. Univ. Al. I. Cuza laşi. Mat., 2004, 50, 159–173 Zbl1070.41014
  11. [11] Wafi A., Khatoon S., Inverse theorem for generalized Baskakov operator, Bull. Calcutta Math. Soc., 2005, 97, 349–360 Zbl1087.41021
  12. [12] You G., Xaun P., Weighted approximation by multidimensional Baskakov operators, J. Math. Res. Exposition, 2000, 20, 43–50 Zbl0954.41013

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