Inequalities related to the Chebychev Functional Involving Integrals Over Different Intervals

Volume 2, Issue 2, 2001

Article 22

INEQUALITIES RELATED TO THE CHEBYCHEV FUNCTIONAL INVOLVING INTEGRALS OVER DIFFERENT INTERVALS

DEPARTMENT OF MATHEMATICS
FACULTY OF TEXTILE TECHNOLOGY
UNIVERSITY OF ZAGREB
CROATIA.
E-Mail: ivanb@zagreb.tekstil.hr

SCHOOL OF COMMUNICATIONS AND INFORMATICS
VICTORIA UNIVERSITY OF TECHNOLOGY
PO BOX 14428
MELBOURNE CITY MC
VICTORIA 8001, AUSTRALIA.
E-Mail: pc@matilda.vu.edu.au

DEPARTMENT OF MATHEMATICS
FACULTY OF TEXTILE TECHNOLOGY
UNIVERSITY OF ZAGREB
CROATIA.
E-Mail: pecaric@mahazu.hazu.hr

Received 22 November, 2000; accepted 03 March, 2001.
Communicated by: G. Anastassiou

ABSTRACT. A generalised Chebychev functional involving integral means of functions over different intervals is investigated. Bounds are obtained for which the functions are assumed to be of Hölder type. A weighted generalised Chebychev functional is also introduced and bounds are obtained in terms of weighted Grüss, Chebychev and Lupas inequalities.

Key words:
Grüss, Chebychev and Lupas inequalities, Hölder.

2000 Mathematics Subject Classification:
26D15, 26D20, 26D99.

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