Volume 3,  Issue 2, 2002

Article 31

AN INEQUALITY IMPROVING THE FIRST HERMITE-HADAMARD INEQUALITY FOR CONVEX FUNCTIONS DEFINED ON LINEAR SPACES AND APPLICATIONS FOR SEMI-INNER PRODUCTS

S.S. DRAGOMIR

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

Received 16 November, 2001; Accepted 15 February, 2002.
Communicated by: C.P. Niculescu

ABSTRACT.   An integral inequality for convex functions defined on linear spaces is obtained which contains in a particular case a refinement for the first part of the celebrated Hermite-Hadamard inequality. Applications for semi-inner products on normed linear spaces are also provided.
Key words:
Hermite-Hadamard integral inequality, Convex functions, Semi-Inner Products.

2000 Mathematics Subject Classification:
Primary 26D15, 26D10; Secondary 46B10.

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