Approximation by α–Bernstein–Schurer–Stancu Operators

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Çetin N., Acu A.

Journal of Mathematical Inequalities, vol.15, no.2, pp.845-860, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.7153/jmi-2021-15-59
  • Journal Name: Journal of Mathematical Inequalities
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.845-860
  • Keywords: Bernstein-Schurer-Stancu operators, alpha-Bernstein operator, modulus of continuity, Voronovskaya type theorem, Gruss-Voronovskaya type theorem, GRUSS-TYPE, INEQUALITIES
  • Ankara Haci Bayram Veli University Affiliated: No

Abstract

© Zagreb Paper JMI-15-59In this paper, we consider a new family of generalized Bernstein-Schurer-Stancu operators, depending on a non-negative real parameter α and study some approximation properties of these operators. We obtain a recurrence formula concerning calculation of moments by Schurer-Stancu operators. We prove a uniform approximation result using the well-known Korovkin theorem and obtain the rate of convergence in terms of modulus of continuity. Also, we present Voronovskaya and Grüss-Voronovskaya type results for these operators. Moreover, we give some numerical examples to illustrate approximation by the new operator.