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q-Bernstein-Type Integral Operators

In: Applications of q-Calculus in Operator Theory

Author

Listed:
  • Ali Aral

    (Kırıkkale University, Department of Mathematics)

  • Vijay Gupta

    (Netaji Subhas Institute of Technology, School of Applied Sciences)

  • Ravi P. Agarwal

    (Texas A&M University-Kingsville, Department of Mathematics)

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.

Suggested Citation

  • Ali Aral & Vijay Gupta & Ravi P. Agarwal, 2013. "q-Bernstein-Type Integral Operators," Springer Books, in: Applications of q-Calculus in Operator Theory, edition 127, chapter 0, pages 113-144, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-6946-9_4
    DOI: 10.1007/978-1-4614-6946-9_4
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