A note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration

AÇIKGÖZ M., Araci S., CANGÜL İ. N.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.707-712, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 218 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.amc.2011.01.091
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.707-712
  • Keywords: Generating function, Bernstein polynomials of several variables, Bernstein operator of several variables, Shift difference operator, Q-difference operator, q-Stirling numbers, q-Volkenborn integration, Hermite polynomials, Carlitz's type q-Bernoulli numbers
  • Bursa Uludag University Affiliated: Yes

Abstract

In this paper, we consider the modified q-Bernstein polynomials for functions of several variables on q-Volkenborn integral and investigate some new interesting properties of these polynomials related to q-Stirling numbers, Hermite polynomials and Carlitz's type q-Bernoulli numbers. (C) 2011 Elsevier Inc. All rights reserved.