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In this work, we study Bernstein-Walsh-type estimations for the derivative of an arbitrary algebraic polynomial in regions with piece wise smooth boundary without cusps of the complex plane. Also, estimates are given on the whole complex plane.
We study the growth rates of the derivatives of an arbitrary algebraic polynomial in bounded and inbounded regions of the complex plane in weighted Lebesgue spaces.
We obtain exact Jackson-type inequalities in terms of the best approximations and averaged values of the generalized moduli of smoothness in the spaces S-p. For classes of periodic functions defined by certain conditions imposed on the average values of the generalized moduli of smoothness, we determine the exact values of the Kolmogorov, Bernstein, linear, and projective widths in the spaces S-p.