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q-Bernstein-Type Integral Operators

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Abstract

In order to approximate integrable functions on the interval [0,1], Kantorovich gave modified Bernstein polynomials. Later in the year 1967 Durrmeyer [58] considered a more general integral modification of the classical Bernstein polynomials, which were studied first by Derriennic [47]. Also some other generalizations of the Bernstein polynomials are available in the literature. The other most popular generalization as considered by Goodman and Sharma [82], namely, genuine Bernstein–Durrmeyer 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

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  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-Bernstein-Type Integral Operators. In: Applications of q-Calculus in Operator Theory. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6946-9_4

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