The present paper discusses in the metricLpS. N. Bernstein type inequalities of the most general kind on very general accessible classes of curves in a complex plane. The obtained estimations, generally speaking, are not improvable.

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Let T denote the interval OE ; . 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 /.