Stancu Type Generalization of Szasz-Durrmeyer Operators Involving Brenke-Type Polynomials

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AKTAŞ R., Soylemez D., TAŞDELEN YEŞİLDAL F.

FILOMAT, cilt.33, sa.3, ss.855-868, 2019 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 33 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.2298/fil1903855a
  • Dergi Adı: FILOMAT
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.855-868
  • Anahtar Kelimeler: Szasz-Durrmeyer operator, modulus of continuity, Brenke type polynomials, Hermite polynomials, MEYER-KONIG, APPROXIMATION
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Ankara Üniversitesi Adresli: Evet

Özet

In the present paper, we introduce a Stancu type generalization of Szasz- Durrmeyer operators including Brenke type polynomials. We give convergence properties of these operators via Korovkin's theorem and the order of convergence by using a classical approach. As an example, we consider a Stancu type generalization of the Durrmeyer type integral operators including Hermite polynomials of variance nu. Then, we obtain the rates of convergence by using the second modulus of continuity. Also, for these operators including Hermite polynomials of variance nu, we present a Voronovskaja type theorem and r-th order generalization of these positive linear operators.