Volume 3,  Issue 1, 2002

Article 4

AN IDENTITY FOR THE CHEBYCHEV FUNCTIONAL AND SOME RAMIFICATIONS

P. CERONE

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

Received 15 April, 2001; 17 July, 2001.
Communicated by: R.P. Agarwal

ABSTRACT.   An identity for the Chebychev functional is presented in which a Riemann-Stieltjes integral is involved. This allows bounds for the functional to be obtained for functions that are of bounded variation, Lipschitzian and monotone. Some applications are presented to produce bounds for moments of functions about a general point g and for moment generating functions.
Key words:
Chebychev functional, Bounds, Riemann-Stieltjes, Moments, Moment Generating Function.

2000 Mathematics Subject Classification:
Primary 26D15, 26D20; Secondary 65Xxx.

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