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The q-derivative and applications to q-Szász Mirakyan operators

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Abstract

By using the properties of the q-derivative, we show that q-Szász Mirakyan operators are convex, if the function involved is convex, generalizing well-known results for q = 1. We also show that q-derivatives of these operators converge to q-derivatives of approximated functions. Futhermore, we give a Voronovskaya-type theorem for monomials and provide a Stancu-type form for the remainder of the q-Szász Mirakyan operator. Lastly, we give an inequality for a convex function f, involving a connection between two nonconsecutive terms of a sequence of q-Szász Mirakyan operators.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Kırıkkale University, Kırıkkale, Turkey

    Ali Aral

  2. School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3, Dwarka, India

    Vijay Gupta

Authors
  1. Ali Aral
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  2. Vijay Gupta
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Aral, A., Gupta, V. The q-derivative and applications to q-Szász Mirakyan operators. Calcolo 43, 151–170 (2006). https://doi.org/10.1007/s10092-006-0119-3

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  • DOI: https://doi.org/10.1007/s10092-006-0119-3

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