Copositive approximation by Hermits extension

Abstract

In this paper, we have found a new expansion of the Hermits polynomial of degree ≤ 3n + 2, n ≥ 1, and by this expansion we have studied the copositive approximation of the functions f in space Lψ ,p (I), 0 < p < 1, and by using the quasi normed space, we presented a development of Whitney theory for the copositive approximation using the modulus of smoothness and average modulus of smoothness τ 3n+3(f,|I|,I) ψ ,p ,n ≥ 1 by using the Hermits polynomial expansion.