Bernstein type operators having 1 and xj as fixed points

Abstract

For certain generalized Bernstein operators {Ln} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions ei(x) = xi and ej (x) = xj are preserved by Ln for each n = 1, 2,… But there exist infinitely many ei such that e0(x) = 1 and ej (x) = xj are its fixed points.