Generalized Bernstein Operators on the Classical Polynomial Spaces Articles uri icon

authors

  • BAYAS ALDAZ, CECILIA ELIZABETH
  • RENDER, H.

publication date

  • December 2018

issue

  • 6

volume

  • 15

International Standard Serial Number (ISSN)

  • 1660-5446

Electronic International Standard Serial Number (EISSN)

  • 1660-5454

abstract

  • We study generalizations of the classical Bernstein operators on the polynomial spaces P-n[a, b], where instead of fixing 1 and x, we reproduce exactly 1 and a polynomial f(1), strictly increasing on [a, b]. We prove that for sufficiently large n, there always exist generalized Bernstein operators fixing 1 and f(1). These operators are defined by non-decreasing sequences of nodes precisely when f(1) > 0 on (a, b), but even if f(1) vanishes somewhere inside (a, b), they converge to the identity.

keywords

  • bernstein polynomial; bernstein operator; convergence