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Szász–Mirakjan–Kantorovich Operators Reproducing Affine Functions: Inverse Results

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Abstract

In a previous paper the author presented a Kantorovich modification of Szász–Mirakjan operators which reproduce affine functions and he provided an upper estimate for the rate of convergence in polynomial weighted spaces. In this paper, for the same family of operators, a strong inverse inequality is given for the case of approximation in norm.

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References

  1. Becker, M.: Global approximation theorems for Szász–Mirakjan and Baskakov operators in polynomial weight spaces. Indiana Math. J 27, 127–142 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bustamante, J.: Szász–Mirakjan–Kantorovich operators reproducing affine functions. Results Math. 75, 130 (2020)

    Article  MATH  Google Scholar 

  3. Bustamante, J.: Baskakov–Kantorovich operators reproducing affine functions: inverse results, to appear

  4. Bustamante, J., Merino-García, J., Quesada, J.M.: Baskakov operators and Jacobi weights: pointwise estimates. J. Inequal. Appl. 119, 17 (2021)

    MathSciNet  MATH  Google Scholar 

  5. Ditzian, Z., Totik, V.: Moduli of Smoothness. Springer, New York (1987)

    Book  MATH  Google Scholar 

  6. Finta, Z.: On converse approximation theorems. J. Math. Anal. Appl. 312, 159–180 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Draganov, B.R., Ivanov, K.G.: Natural weights for uniform approximation by the Szász–Mirakjan operator, Constructive theory of functions, 57–82. Prof. M. Drinov Acad. Publ. House, Sofia (2014)

  8. Zhou, D.X.: Weighted approximation by Szász–Mirakjan operators. J. Approx. Theory 76, 393–402 (1994)

    Article  MathSciNet  MATH  Google Scholar 

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  1. Facultad de Ciencias Físico-Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 1152, C.P. 72000, Puebla, PUE, Mexico

    Jorge Bustamante

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  1. Jorge Bustamante
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Correspondence to Jorge Bustamante.

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Bustamante, J. Szász–Mirakjan–Kantorovich Operators Reproducing Affine Functions: Inverse Results. Results Math 78, 189 (2023). https://doi.org/10.1007/s00025-023-01947-x

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  • DOI: https://doi.org/10.1007/s00025-023-01947-x

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