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The Order of Best Approximation in Some Classes of Functions

Authors:	Sorin G> Gal

Institution:	(1) Department of Mathematics, University of Oradea, Str. Armatei Române 5, 3700 Oradea, Romania

Abstract:	Starting from the equivalence between the Ditzian–Totik modulus $\omega _1^\varphi \left( {f;\delta } \right)_\infty$ and $\omega _1 \left( {g;\delta } \right)_\infty$ , where $g\left( t \right) = f\left( {\cos t} \right)$ , in this article large classes of functions are introduced for which the modulus $\omega _1 \left( {g;\delta } \right)_\infty$ can be easily calculated. As a consequence, very good estimates for the bestapproximation are obtained. The attempts to estimate or calculate themodulus $\omega _{_1 }^\varphi \left( {f;\delta } \right)_\infty$ can be a very intricateproblem.

Keywords:	best approximation by polynomials Jackson type estimates moduli of smoothness calculation of the modulus of continuity convex functions
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