On approximation properties of generalized Lupaş type operators based on Polya distribution with Pochhammer k-symbol

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GÜREL YILMAZ Ö., AKTAŞ R., Taşdelen F., Olgun A.

Hacettepe Journal of Mathematics and Statistics, cilt.51, sa.2, ss.338-361, 2022 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.15672/hujms.911716
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.338-361
  • Anahtar Kelimeler: Bernstein operators, Stancu operators, Lupas operators, Kantorovich operators, Polya distribution, modulus of continuity, Lipschitz class, Voronovskaja type theorem, Pochhammer k-symbol, SMOOTHNESS PROPERTIES, BERNSTEIN, CONVERGENCE, SEQUENCES
  • Ankara Üniversitesi Adresli: Evet

Özet

The purpose of this paper is to introduce a Kantorovich variant of Lupaş-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k.