A NUMERICAL COMPARATIVE STUDY OF GENERALIZED BERNSTEIN-KANTOROVICH OPERATORS

Kadak U., ÖZGER F.

MATHEMATICAL FOUNDATIONS OF COMPUTING, vol.4, no.4, pp.311-332, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.3934/mfc.2021021
  • Journal Name: MATHEMATICAL FOUNDATIONS OF COMPUTING
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.311-332
  • Keywords: Multiple shape parameter, infinite matrices, Lipschitz continuous func-tion, Voronovskaja asymptotic formula, Maple algorithm, STATISTICAL APPROXIMATION, DIFFERENCE OPERATOR, SUMMABILITY, CONVERGENCE, POLYNOMIALS, KOROVKIN, THEOREMS
  • Gazi University Affiliated: Yes

Abstract

In this paper, a new generalization of the Bernstein-Kantorovich type operators involving multiple shape parameters is introduced. Certain Voronovskaja and Gru spacing diaeresis ss-Voronovskaya type approximation results, statistical convergence and statistical rate of convergence of proposed operators are obtained by means of a regular summability matrix. Some illustrative graphics that demonstrate the convergence behavior, accuracy and consistency of the operators are given via Maple algorithms. The proposed operators are comprehensively compared with classical Bernstein, Bernstein-Kantorovich and other new modifications of Bernstein operators such as lambda-Bernstein, lambda-Bernstein-Kantorovich, alpha-Bernstein and alpha-Bernstein-Kantorovich operators.