Volume 2,  Issue 3, 2001

Article 28

ON SOME GENERALIZATIONS OF STEFFENSEN'S INEQUALITY AND RELATED RESULTS

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 8 January, 2001; accepted 19 March, 2001.
Communicated by: H. Gauchman

ABSTRACT. Steffensen's inequality is generalised to allow bounds involving any two subintervals rather than restricting them to include the end points. Further results are obtained involving an identity related to the generalised Chebychev functional in which the difference of the mean of the product of functions and the product of means of functions over different intervals is utilised. Bounds involving one subinterval are also presented.

Key words:
Steffensen's Inequality, Chebychev functional.

2000 Mathematics Subject Classification:
26D15, 26D10, 26D99.

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