Dunkl generalization of Szasz operators via q-calculus

Icoz G., ÇEKİM B.

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

  • Publication Type: Article / Article
  • Publication Date: 2015
  • Doi Number: 10.1186/s13660-015-0809-y
  • Journal Name: JOURNAL OF INEQUALITIES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Dunkl analog, generating functions, Szasz operator, generalization of exponential function, Q-BERNSTEIN POLYNOMIALS, APPROXIMATION PROPERTIES, CONVERGENCE
  • Gazi University Affiliated: Yes

Abstract

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.