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ABSTRACT.
M. and S. Izumi [2] and the present author [7] have extended certain theorems of R.P. Boas [1] concerning
the Fourier coefficients of functions belonging to the Lipschitz classes. Very recently L. Leindler [6] has given further generalization using the so called quasi power-monotone sequences. The
goal of the present work is to further prove theorems similar to those of L. Leindler.
[1] R.P. BOAS Jr.,
Fourier series with positive coefficients, J.
Math. Anal. Appl., 17
(1967), 463–483.
[2] M. IZUMI and S.
IZUMI, Lipschitz classes and Fourier coefficients, J.
Math. Mech.,
18 (1969),
857–870.
[6] L. LEINDLER, Power-monotone sequences and Fourier series
with positive coefficients, J. Inequal. Pure
Appl. Math., 1(1) (2000), Article 1, http://jipam.vu.edu.au/v1n1/001_99.html.
[7] J.
NEMETH, Fourier series with positive coefficients and
generalized Lipschitz classes, Math.
54
(1990), 291–304.
Key words:
Fourier series,
Fourier
coefficients, modulus of
continuity,
quasi power-monotone sequences.
2000 Mathematics Subject
Classification:
26A16, 26A15,
40A05.
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