Approximation properties of Lupas-Kantorovich operators based on Polya distribution

Agrawal P. N., İSPİR N., Kajla A.

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, cilt.65, sa.2, ss.185-208, 2016 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Sayı: 2
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1007/s12215-015-0228-4
  • Dergi Adı: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.185-208
  • Anahtar Kelimeler: Asymptotic formula, Local approximation, Global approximation, Polya distribution
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we introduce Kantorovich modification of the operators considered by Lupas and Lupas (Stud Univ Babes-Bolyai Math 32(4):61-69, 1987) based on Polya distribution and study Voronovskaja type asymptotic formula, local approximation, pointwise estimates and global approximation results. In the last section, we consider the bivariate generalization of these operators and discuss the rate of convergence. We also illustrate the convergence of these operators to some functions by graphics in Maple for both one and two dimensional cases and also estimate the error in the approximation by giving numerical examples for the bivariate case.