Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions

OLGUN A., İNCE İLARSLAN H. G., Tasdelen F.

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, cilt.21, sa.3, ss.209-221, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.2478/auom-2013-0053
  • Dergi Adı: ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.209-221
  • Anahtar Kelimeler: Positive Linear operators, Kantorovich-type operators, Meyer-Konig and Zeller operators, Modulus of contiunity, Modified Lipschitz class, r-th order generalization, BERNSTEIN POWER-SERIES, STATISTICAL APPROXIMATION
  • Gazi Üniversitesi Adresli: Evet

Özet

In the present paper, we study a Kantorovich type generalization of Meyer-Konig and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0, Lambda], 0 < Lambda < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.