LAUSR

Let N be an integer greater than or equal to 2 and let xi′s be numbers with x0 < x1 < x2 < ⋯ < xN. Denote that I is the interval [x0,xN] and Δ = {(xk,μk) ∈ ℝ × ℝ : k = 0, 1,…,N} is a set of points. Suppose that Yk is a random perturbation of μk for k = 0, 1,…,N, and we set Δ∗ = {(x k,Yk) : k = 0, 1,…,N}. Let fΔ and fΔ∗ be linear fractal interpolation functions on I corresponding to the set of points Δ and Δ∗, respectively. The value fΔ∗(x) is random for all x ∈ I. In this paper, we show that the expectation of fΔ∗(x) is fΔ(x). We also establish estimations for the variance of fΔ∗(x) and the expectation of |fΔ∗(x) − fΔ(x)|.