Trigonometric approximation of periodic functions belonging to weighted Lipschitz class W(Lp, Ψ(t), β)

Recently, the authors introduced a new function class Lip(omega(t),p), where omega(t) is an increasing function, and determined the error of approximation of f is an element of Lip(omega(t),p) through matrix means of its Fourier series [Trigonometric approximation of periodic functions belonging to Lip(omega(t),p)-class, J. Comput. Appl. Math. 270 (2014) 223-230]. In this paper, we define W(L-p, Psi(t), beta), a weighted version of Lip(omega(t),p), with weight function sin(beta P)(x/2) and determine the error of approximation of f is an element of W(L-p, Psi(t), beta). We also derive some corollaries from our results.