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Shape Preserving Properties for -Bernstein-Stancu Operators

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  • Yali Wang
  • Yinying Zhou

Abstract

We investigate shape preserving for -Bernstein-Stancu polynomials introduced by Nowak in 2009. When , reduces to the well-known -Bernstein polynomials introduced by Phillips in 1997; when , reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; when , , we obtain classical Bernstein polynomials. We prove that basic basis is a normalized totally positive basis on and -Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on .

Suggested Citation

  • Yali Wang & Yinying Zhou, 2014. "Shape Preserving Properties for -Bernstein-Stancu Operators," Journal of Mathematics, Hindawi, vol. 2014, pages 1-5, May.
    • Handle: RePEc:hin:jjmath:603694
    DOI: 10.1155/2014/603694
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