Approximation by Durrmeyer-type operators

Vijay Gupta; G. S. Srivastava

Annales Polonici Mathematici (1996)

  • Volume: 64, Issue: 2, page 153-159
  • ISSN: 0066-2216

Abstract

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We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.

How to cite

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Vijay Gupta, and G. S. Srivastava. "Approximation by Durrmeyer-type operators." Annales Polonici Mathematici 64.2 (1996): 153-159. <http://eudml.org/doc/269980>.

@article{VijayGupta1996,
abstract = {We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.},
author = {Vijay Gupta, G. S. Srivastava},
journal = {Annales Polonici Mathematici},
keywords = {modulus of smoothness; global direct theorem; differential and integral operators; Ditzian-Totik modulus of smoothness},
language = {eng},
number = {2},
pages = {153-159},
title = {Approximation by Durrmeyer-type operators},
url = {http://eudml.org/doc/269980},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Vijay Gupta
AU - G. S. Srivastava
TI - Approximation by Durrmeyer-type operators
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 2
SP - 153
EP - 159
AB - We define a new kind of Durrmeyer-type summation-integral operators and study a global direct theorem for these operators in terms of the Ditzian-Totik modulus of smoothness.
LA - eng
KW - modulus of smoothness; global direct theorem; differential and integral operators; Ditzian-Totik modulus of smoothness
UR - http://eudml.org/doc/269980
ER -

References

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  1. [1] M. M. Derriennic, Sur l'approximation de fonctions intégrables sur [0,1] par des polynômes de Bernstein modifiés, J. Approx. Theory 31 (1981), 325-343. Zbl0475.41025
  2. [2] Z. Ditzian and K. Ivanov, Bernstein type operators and their derivatives, J. Approx. Theory 56 (1989), 72-90. 
  3. [3] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer Ser. Comput. Math. 9, Springer, Berlin, 1987. 
  4. [4] J. L. Durrmeyer, Une formule d'inversion de la transformée de Laplace: Applications à la théorie des moments, Thèse de 3e Cycle, Faculté des Sciences de l'Université de Paris, 1967. 
  5. [5] V. Gupta, A note on modified Baskakov type operators, Approx. Theory Appl. 10 (1994), 74-78. Zbl0823.41021
  6. [6] M. Heilmann, Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl. 5 (1989), 105-127. Zbl0669.41014
  7. [7] H. S. Kasana, P. N. Agrawal and V. Gupta, Inverse and saturation theorems for linear combination of modified Baskakov operators, Approx. Theory Appl. 7 (1991), 65-82. Zbl0755.41024
  8. [8] S. M. Mazhar and V. Totik, Approximation by modified Szász operators, Acta Sci. Math. (Szeged) 49 (1985), 257-269. Zbl0611.41013
  9. [9] A. Sahai and G. Prasad, On simultaneous approximation by modified Lupas operators, J. Approx. Theory 45 (1985), 122-128. Zbl0596.41035
  10. [10] R. P. Sinha, P. N. Agrawal and V. Gupta, On simultaneous approximation by modified Baskakov operators, Bull. Soc. Math. Belg. Sér. B 42 (1991), 217-231. Zbl0762.41022

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