Bernstein type operators having 1 and x j as fixed points

For certain generalized Bernstein operators {L _n } we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e _i (x) = x ⁱ and e _j (x) = x ^j are preserved by L _n for each n = 1, 2,… But there exist infinitely many e _i such that e ₀(x) = 1 and e _j (x) = x _j are its fixed points.