Approximation properties of lambda-Kantorovich operators

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Acu A., Manav N., Sofonea D. F.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1186/s13660-018-1795-7
  • Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Kantorovich operators, Bernstein operator, Voronovskaja theorem, Rate of convergence, THEOREM
  • Gazi Üniversitesi Adresli: Evet

Özet

In the present paper, we study a new type of Bernstein operators depending on the parameter lambda is an element of [-1, 1]. The Kantorovich modification of these sequences of linear positive operators will be considered. A quantitative Voronovskaja type theorem by means of Ditzian-Totik modulus of smoothness is proved. Also, a Gruss-Voronovskaja type theorem for lambda-Kantorovich operators is provided. Some numerical examples which show the relevance of the results are given.