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 L_ψ,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.

Subject Classification: 2000:

• 41A10
• 41A50

Keywords:

• Modulus of smoothness
• Average modulus of smoothness
• Whitney theory
• Hermits polynomial