Volume 2,  Issue 2, 2001

Article 14

POWER-MONOTONE SEQUENCES AND FOURIER SERIES WITH POSITIVE COEFFICIENTS

J. NEMETH

BOLYAI INSTITUTE, 
UNIVERSITY OF SZEGED, 
ARADI VÉRTANÚK TERE 1.
6720 SZEGED, HUNGARY
E-Mail: nemethj@math.u-szeged.hu

Received 25 July, 2000; accepted 10 August, 2000.
Communicated by: L. Leindler


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.


Download this article (PDF):

Suitable for a printer:    

Suitable for a monitor:        

To view these files we recommend you save them to your file system and then view by using the Adobe Acrobat Reader. 

That is, click on the icon using the 2nd mouse button and select "Save Target As..." (Microsoft Internet Explorer) or "Save Link As..." (Netscape Navigator).

See our PDF pages for more information.

Other papers in this issue

Power-Monotone Sequences and Fourier Series with Positive Coefficients
J. Nemeth

On Some Fundamental Integral Inequalities and their Discrete Analogues
B.G.  Pachpatte

Subharmonic Functions and their Riesz Measure
Raphaele Supper

A Priori Estimate for a System of Differential Operators
Chikh Bouzar

Improved Inclusion-Exclusion Inequalities for Simplex and Orthant Arrangements
Daniel Q. Naiman and Henry P. Wynn

Monotonic Refinements of a Ky Fan Inequality
Kwok K. Chong

Sub-super Solutions and the Existence of Extremal Solutions in Noncoercive Variational Inequalities
V.K. Le

Refinements of Carleman's Inequality
Bao-Quan Yuan 

Inequalities related to the Chebychev Functional Involving Integrals Over Different Intervals
I. Budimir, P. Cerone, and  J. Pecaric

Some Distortion Inequalities Associated with the Fractional Derivatives of Analytic and Univalent Functions
H.M. Srivastava, Yi Ling and Gejun Bao

Necessary and Sufficient Condition for Existence and Uniqueness of the Solution of Cauchy Problem for Holomorphic Fuchsian Operators
Mekki Terbeche

Bounds for Entropy and Divergence for Distributions over a Two-Element Set
Flemming Topsoe

A Pick Function Related to an Inequality for the Entropy Function
Christian Berg


Other issues

 

 

 

© 2000 School of Communications and Informatics, Victoria University of Technology. All rights reserved.
JIPAM is published by the School of Communications and Informatics which is part of the Faculty of Engineering and Science, located in Melbourne, Australia. All correspondence should be directed to the editorial office.

Copyright/Disclaimer