IJPAM: Volume 44, No. 4 (2008)


I.M.R. Pinheiro
P.O. Box 12396, A'Beckett st, Melbourne
Victoria, 8006, AUSTRALIA
e-mail: mrpprofessional@yahoo.com

Abstract.In this one more paper on $S-$convexity, we referee, on the top of everyone else, the lower bound, proposed by S. Fitzpatrick et al, for $K^{2}_{s}$, by applying our own work to their earlier deductions. On the top of that, we define $H-H$ results also for $K^{1}_{s}$ and write a bit about why $S_{1}-$convexity is not a proper extension of the concept of convexity in what regards the set of the real numbers, but $S_{2}$ is. And, as a side result, we get to improve the range of choices for the Hermite-Hadamard inequality bounds, in terms of constants.

Received: March 2, 2008

AMS Subject Classification: 26D10, 26D15

Key Words and Phrases: Hermite-Hadamard, inequality, lower bound, upper bound, Sever Dragomir, Fitzpatrick, Hermite, Hadamard, $S-$convexity, convexity,
$S-$convex, convex

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 44
Issue: 4