Extended Bernstein-Kantorovich-Stancu Operators with Multiple Parameters and Approximation Properties

Kadak U., Ozluk M.

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, cilt.42, sa.5, ss.523-550, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 5
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/01630563.2021.1895833
  • Dergi Adı: NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.523-550
  • Anahtar Kelimeler: Bernstein-Kantorovich operator, Lipschitz continuous functions, modulus of continuity, rate of convergence, Stancu operators, Voronovskaja asymptotic formula, MODULAR FUNCTION-SPACES, STATISTICAL CONVERGENCE, SUMMABILITY
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Gruss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover, using Ditzian-Totik moduli, local and global approximation properties associated to the proposed operator have been established. Finally, several illustrative examples are presented to demonstrate the efficiency, applicability and validity of the operator. The graphical and numerical results verify that the proposed operator gives better approximation as well as expand the previous Bernstein-Kantorovich type modifications including single parameter.