@article{article_1723278, title={Some Estimates of the Growth of Polynomials in the Region with Piecewise Smooth Boundary}, journal={Cumhuriyet Science Journal}, volume={46}, pages={572–582}, year={2025}, DOI={10.17776/csj.1723278}, author={Gün, Cevahir Doğanay}, keywords={Bernstein inequality, polynomial estimates, quasiconformal curve, piecewise smooth curve}, abstract={In this paper, we investigate inequalities for higher order derivatives of algebraic polynomials in weighted Lebesgue space. In doing so, using the weighted L_p-norm, we establish the growth of the modulus of the m-th derivatives of algebraic polynomials on the closure and outside of a given region of the complex plane bounded by a piecewise smooth curve with interior zero angles. As a result, we estimate the growth rate of the derivatives of algebraic polynomials on the whole complex plane depending on the parameters of the region under consideration.}, number={3}, publisher={Sivas Cumhuriyet University}