COMBINATORIAL INEQUALITIES AND SUMS INVOLVING BERNSTEIN POLYNOMIALS AND BASIS FUNCTIONS

ŞİMŞEK Y.

JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS, vol.8, no.3, pp.15-24, 2017 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 3
  • Publication Date: 2017
  • Journal Name: JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.15-24
  • Keywords: Bernstein basis functions, Bernstein polynomials, Bernoulli numbers, Bernoulli polynomials, Stirling numbers, Combinatorial sum, Combinatorial inequalities, Generating functions
  • Akdeniz University Affiliated: Yes

Abstract

By using the Bernstein basis functions and Bernstein operator with their integral, we derive some combinatorial sums and identities including the Bernoulli numbers and polynomials, the Stirling numbers of the second kind and also some relations. Moreover, we give some inequalities involving combinatorial numbers and binomial coefficients.