#### Glasnik Matematicki, Vol. 40, No.1 (2005), 133-138.

### A REMARK ON CONCENTRATION OF THE ERROR BETWEEN
A FUNCTION AND ITS BEST POLYNOMIAL APPROXIMANTS. II: A PROBLEM
OF HASSON

### J. L. Wang and S. P. Zhou

Department of Mathematics, Shaoxing Arts and Science College,
Shaoxing, Zhejiang 312000, China

Institute of Mathematics, Zhejiang University of Sciences,
Xiasha Economic Development Area, Hangzhou, Zhejiang 310018,
China

*e-mail:* `szhou@nbip.net`

*e-mail:* `szhou@zjip.com`

**Abstract.** In the present paper we construct a function
to give a positive answer to a problem raised by Hasson,
that says, the conclusion of a result cannot be
strengthened.

**2000 Mathematics Subject Classification.**
41A17, 41A25, 41A50.

**Key words and phrases.** Approximation, construction,
Chebyshev polynomial.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.40.1.12

**References:**

- N.I. Akhiezer,
Theory of Approximation, Ungar, New York, 1956.

- G. Freud,
*Eine Ungleichung für Tschebyscheffsche
Approximations-polynome*,
Acta Sci. Math. **19** (1958), 162-164.

- M. Ganzburg,
*Moduli of smoothness and best approximation
of functions with singularities*,
Computers & Mathematics **40** (2000), 219-242.

- M. Hasson,
*Concentration of the error between a function
and its polynomial of best uniform approximation*,
Proc. Edinburgh Math. Soc. **41** (1998), 447-463.

- S. B. Stechkin,
*On the order of the best approximations of
continuous functions*,
Izv. Akad. Nauk SSSR **15** (1951), 219-242 (in Russian).

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