On an Open Problem of Bai-Ni Guo and Feng Qi

Volume 4, Issue 2, 2003

Article 29

ON AN OPEN PROBLEM OF BAI-NI GUO AND FENG QI

ZIVORAD TOMOVSKI AND KOSTADIN TRENCEVSKI

INSTITUTE OF MATHEMATICS,
ST. CYRIL AND METHODIUS UNIVERSITY,
P. O. BOX 162, 1000 SKOPJE,
MACEDONIA.
E-Mail: tomovski@iunona.pmf.ukim.edu.mk

E-Mail: kostatre@iunona.pmf.ukim.edu.mk

Received 17 September, 2002; Accepted 28 March, 2003.
Communicated by: F. Qi

ABSTRACT. In this paper, an open problem posed respectively by B.-N. Guo and F. Qi in [4,6,7] is partially solved: an integral expression and a new double inequality of the generalized Mathieu's series $% \sum_{n=1}^{\infty}{\frac{2n}{(n^2+a^2)^{p+1}}}$ are established by using some properties of gamma function and Fourier transform inequalities, where

, $p\in \mathbb{N}$ .

Key words:
Integral expression, Inequality, Mathieu's series, gamma function, Fourier transform inequality.

2000 Mathematics Subject Classification:
Primary 26D15, 33E20; Secondary 40A30.

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