A Variant of Jensen's Inequality

Volume 4, Issue 4, 2003

Article 73

A VARIANT OF JENSEN'S INEQUALITY

A.McD. MERCER

DEPARTMENT OF MATHEMATICS AND STATISTICS,
UNIVERSITY OF GUELPH,
GUELPH, ONTARIO N1G 2W1,
CANADA.
E-Mail: amercer@reach.net

Received 14 August, 2003 Accepted 27 August, 2003.
Communicated by: P.S. Bullen

ABSTRACT. If

is a convex function the following variant of the classical Jensen's Inequality is proved

$\displaystyle f\left( x_{1}+x_{n}-\sum w_{k}k_{k}\right) \leq f(x_{1})+f(x_{n})-\sum w_{k}f(x_{k}).$

Key words:
Jensen's inequality, Convex functions..

2000 Mathematics Subject Classification:
26D15.

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