Dunkl generalization of Szasz operators via q-calculus

Icoz G., ÇEKİM B.

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1186/s13660-015-0809-y
  • Dergi Adı: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Dunkl analog, generating functions, Szasz operator, generalization of exponential function, Q-BERNSTEIN POLYNOMIALS, APPROXIMATION PROPERTIES, CONVERGENCE
  • Gazi Üniversitesi Adresli: Evet

Özet

We construct the linear positive operators generated by the q-Dunkl generalization of the exponential function. We have approximation properties of the operators via a universal Korovkin-type theorem and a weighted Korovkin-type theorem. The rate of convergence of the operators for functions belonging to the Lipschitz class is presented. We obtain the rate of convergence by means of the classical, second order, and weighted modulus of continuity, respectively, as well.