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q-Discrete Operators and Their Results

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Applications of q-Calculus in Operator Theory

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Abstract

This chapter deals with the q-analogue of some discrete operators of exponential type. We study some approximation properties of the q-Bernstein polynomials, q-Szász–Mirakyan operators, q-Baskakov operators, and q-Bleimann, Butzer, and Hahn operators. Here, we present moment estimation, convergence behavior, and shape-preserving properties of these discrete operators.

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Authors and Affiliations

  1. Department of Mathematics, Kırıkkale University, Yahşihan, Kirikkale, Turkey

    Ali Aral

  2. School of Applied Sciences, Netaji Subhas Institute of Technology, New Delhi, India

    Vijay Gupta

  3. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, Texas, USA

    Ravi P. Agarwal

Authors
  1. Ali Aral
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  2. Vijay Gupta
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  3. Ravi P. Agarwal
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Aral, A., Gupta, V., Agarwal, R.P. (2013). q-Discrete Operators and Their Results. In: Applications of q-Calculus in Operator Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6946-9_2

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