Approximation by algebraic polynomials in metric spaces $$$L_{\psi}$$$

T.A. Agoshkova (Dnipropetrovsk National University of Railway Transport named after Academician V. Lazaryan),


In the space $$$L_{\psi}[-1;1]$$$ of non-periodic functions with metric $$$\rho(f,0)_{\psi} = \int\limits_{-1}^1 \psi(|f(x)|)dx$$$, where $$$\psi$$$ is a function of the type of modulus of continuity, we study Jackson inequality for modulus of continuity of $$$k$$$-th order in the case of approximation by algebraic polynomials. It is proved that the direct Jackson theorem is true if and only if the lower dilation index of the function $$$\psi$$$ is not equal to zero.


the direct Jackson theorem; modulus of continuity; modulus of continuity of k-th order; the lower dilation index; an algebraic polynomial


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