Authors:
Jorge Bustamante Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, México

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Abisaí Carrillo-Zentella Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, México

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José M. Quesada Departamento de Matemáticas, Universidad de Jaén, Jaén, Spain

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Abstract

We present direct and strong converse theorems for a general sequence of positive linear operators satisfying some functional equations. The results can be applied to some extensions of Baskakov and Szász–Mirakyan operators.

  • [1] Becker, M. 1978 Global approximation theorems for Szász–Mirakjan and Baskakov operators in polynomial weight spaces Indiana Math. J. 27 127142 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [2] Bustamante, J. 2008 Estimates of positive linear operators in terms of second-order moduli J. Math. Anal. Appl. 345 203212 .

  • [3] Ditzian, Z. 1994 Direct estimate for Bernstein polynomials J. Approx. Theory 79 165166 .

  • [4] Ditzian, Z. Ivanov, K. G. 1993 Strong converse inequalities J. Anal. Math. 61 61111 .

  • [5] Ditzian, Z. Totik, V. 1987 Moduli of Smoothness Springer New York .

  • [6] Felten, M. 1998 Local and global approximation theorems for positive linear operators J. Approx. Theory 94 396419 .

  • [7] Finta, Z. 2005 On converse approximation theorems J. Math. Anal. Appl. 312 159180 .

  • [8] Guo, S. Tong, H. Zhang, G. 2002 Stechkin–Marchaud-type inequalities for Baskakov polynomials J. Approx. Theory 114 3347 .

  • [9] Guo, S. Qi, Q. 2003 Strong converse inequalities for Baskakov operators J. Approx. Theory 124 219231 .

  • [10] Haase, M. 2007 Convexity inequalities for positive operators Positivity 11 5768 .

  • [11] Impens, Ch. Gavrea, I. 2002 A Leibniz differentiation formula for positive operators J. Math. Anal. Appl. 271 175181 .

  • [12] Knoop, H. B. Zhou, X. L. 1994 The lower estimate for linear positive operators (II) Resultate Math. 25 315330.

  • [13] Lan, Qi Qiu 2002 The strong converse inequalities for generalized Baskakov-type operators Pure Applied Math. 18 49 317321 in Chinese.

    • Search Google Scholar
    • Export Citation
  • [14] Sikkema, P. C. 1970 On some linear positive operators Indag. Math. 32 327337.

  • [15] Totik, V. 1994 Strong converse inequalities J. Approx. Theory 76 369375 .

  • [16] Totik, V. 1994 Approximation by Bernstein polynomials Amer. J. Math. 116 9951018 .

  • [17] Volkov, Yu. I. 1978 Certain positive linear operators Math. Notes 23 363368 .

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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