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Approximation of Discontinuous Functions by q-Bernstein Polynomials

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Mathematical Analysis, Approximation Theory and Their Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 111))

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Abstract

This chapter presents an overview of the results related to the q-Bernstein polynomials with q > 1 attached to discontinuous functions on [0, 1]. It is emphasized that the singularities of such functions located on the set

$$\displaystyle{\mathbb{J}_{q}:=\{ 0\} \cup \{ q^{-l}\}_{ l=0}^{\infty },\;\;q> 1,}$$

are definitive for the investigation of the convergence properties of their q-Bernstein polynomials.

In the memory of Professor Hüseyin Şirin Hüseyin

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Acknowledgement

We would like to express our sincere appreciation to Mr. P. Danesh from Atilim University Academic Writing and Advisory Center for his valuable help in the preparation of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Atilim University, TR-06836 İncek, Ankara, Turkey

    Sofia Ostrovska & Ahmet Yaşar Özban

Authors
  1. Sofia Ostrovska
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  2. Ahmet Yaşar Özban
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Corresponding author

Correspondence to Sofia Ostrovska .

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Editors and Affiliations

  1. Department of Mathematics, National Technical Unversity of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Department of Mathematics, Netaji Subhas Instit. of Tech., New Delhi, India

    Vijay Gupta

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Ostrovska, S., Özban, A.Y. (2016). Approximation of Discontinuous Functions by q-Bernstein Polynomials. In: Rassias, T., Gupta, V. (eds) Mathematical Analysis, Approximation Theory and Their Applications. Springer Optimization and Its Applications, vol 111. Springer, Cham. https://doi.org/10.1007/978-3-319-31281-1_22

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