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Direct estimates for certain Szász type operators

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  • Gupta, Vijay
  • Rassias, Themistocles M.

Abstract

The present paper deals with the modified forms of the Szász basis functions. We propose a Durrmeyer type operator having the basis functions in summation and integration due to Jain (1972) and Paˇltaˇnea (2008). We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation. In the end, we give an open problem for the readers.

Suggested Citation

  • Gupta, Vijay & Rassias, Themistocles M., 2015. "Direct estimates for certain Szász type operators," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 469-474.
    • Handle: RePEc:eee:apmaco:v:251:y:2015:i:c:p:469-474
    DOI: 10.1016/j.amc.2014.11.078
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    References listed on IDEAS

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    1. Gradimir Milovanović & Michael Rassias, 2013. "Some properties of a hypergeometric function which appear in an approximation problem," Journal of Global Optimization, Springer, vol. 57(4), pages 1173-1192, December.
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    Cited by:

    1. Kajla, Arun & Agrawal, P.N., 2015. "Szász–Durrmeyer type operators based on Charlier polynomials," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 1001-1014.
    2. Xu, Xiao-Wei, 2015. "Semigroup structural form for Bernstein-type operators and its applications," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 923-934.

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