D-monotone approximation in Lp,w([−1, 1]d)

The objective of this work is studied approximation d-monotone unbounded function in weighted space by using some types of algebraic polynomials of degree ≤ d − 1 which interpolates a d-monotone function f and d knot, sufficiently approximations it, even if the knot of interpolation are close to each other moreover, we are establish the degree of approximation of d-monotone mappings in collection Lp,w(x), 1 ≤ p < ∞ in terms modulus of smoothness and the average modulus of smoothness τd weighted space.