Abstract
Let T denote the interval . In this paper, some theorems for approximation by trigonometric polynomials in the Orlicz space are proved. Under certain conditions, we prove the existence of derivatives of functions belonging to the Orlicz space 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 .
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