Hilbert-Pachpatte Type Integral Inequalities and their Improvement

Volume 4, Issue 1, 2003

Article 16

HILBERT-PACHPATTE TYPE INTEGRAL INEQUALITIES AND THEIR IMPROVEMENT

SCHOOL OF COMPUTER SCIENCE AND MATHEMATICS
VICTORIA UNIVERSITY OF TECHNOLOGY
PO BOX 14428
MELBOURNE CITY MC
VICTORIA 8001, AUSTRALIA.
E-Mail: sever@matilda.vu.edu.auURL: http://rgmia.vu.edu.au/SSDragomirWeb.html

DEPARTMENT OF APPLIED MATHEMATICS
CHANGWON NATIONAL UNIVERSITY
CHANGWON 641-773, KOREA.
E-Mail: yhkim@sarim.changwon.ac.kr

Received 31 October, 2002; Accepted 8 January, 2003.
Communicated by: P.S. Bullen

ABSTRACT. In this paper, we obtain an extension of multivariable integral inequality of Hilbert-Pachpatte type. By specializing the upper estimate functions in the hypothesis and the parameters, we obtain many special cases.

Key words:
Hilbert's inequality, Hilbert-Pachpatte type inequality, Hölder's inequality, Jensen inequality.

2000 Mathematics Subject Classification:
26D15.

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