On approximation by trigonometric polynomials in Orlicz spaces

Let T denote the interval [-pi, pi]. In this paper, some theorems for approximation by trigonometric polynomials in the Orlicz space L-M(T) are proved. Under certain conditions, we prove the existence of derivatives of functions belonging to the Orlicz space L-M(T) and investigate the approximation properties of the derivatives of trigonometric polynomials. Note that the estimate obtained between the derivatives of functions and the derivatives of trigonometric polynomials depends on a sequence of best approximations in the Orlicz space L-M(T)