The Order of Best Approximation in Some Classes of Functions
Tóm tắt
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
$$f$$
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.
Tài liệu tham khảo
Z. Ditzian and V. Totik, Moduli of Smoothness, Springer–Verlag, Berlin, 1987.
S. G. Gal, Calculus of the modulus of continuity for nonconcave functions and applications, Calcolo 27, 195–202 (1990).
S. G. Gal, On the order of best approximation in some subclasses of functions, Babes–Bolyai University, Research Seminars, Sem. Math. Anal. 7, 5–13 (1994).
G. Mastroianni and P. Vértesi, Approximation by some operators using certain new moduli of continuity, Suppl. Rend. Circ. Mat. Palermo 33, 387–397 (1993).
G. G. Lorentz, Approximation of Functions, 2nd edn., Chelsea, New York, 1985.