Trigonometric approximation in Lp-norm

We shall weaken the conditions of monotonicity given by Chandra [J. Math. Anal. Appl. 275 (2002) 13-26], where he investigated trigonometrical polynomials associated with f∈Lip(α,p) (0<α⩽1, p⩾1) to approximate f in Lp-norm to the degree of O(n−α) (0<α⩽1).