Generalization of Szasz operators involving Brenke type polynomials


Varma S., Sucu S., İÇÖZ G.

COMPUTERS & MATHEMATICS WITH APPLICATIONS, vol.64, no.2, pp.121-127, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 64 Issue: 2
  • Publication Date: 2012
  • Doi Number: 10.1016/j.camwa.2012.01.025
  • Journal Name: COMPUTERS & MATHEMATICS WITH APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.121-127
  • Keywords: Szasz operator, Modulus of continuity, Rate of convergence, Brenke type polynomials, Gould-Hopper polynomials
  • Gazi University Affiliated: Yes

Abstract

The purpose of this paper is to give a generalization of Szasz operators defined by means of the Brenke type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre's K-functional. An explicit example with our operators including Gould-Hopper polynomials which generalize Szasz operators in a natural way is given. (C) 2012 Elsevier Ltd. All rights reserved.