IJPAM: Volume 69, No. 1 (2011)

MORE ON CAUCHY'S MEANS AND GENERALIZATION OF
HADAMARD INEQUALITY VIA CONVERSES OF
JENSEN'S INEQUALITY AND SUPERQUADRACITY

S. Abramovich$^1$, G. Farid$^2$, S. Ivelić$^3$, J. Pečarić$^4$
$^1$Department of Mathematics
University of Haifa
Haifa, ISRAEL
e-mail: abramos@math.haifa.ac.il
$^{2,4}$Abdus Salam School of Mathematical Sciences
GC University
Lahore, 54000, PAKISTAN
$^2$e-mail: faridphdsms@hotmail.com
$^3$Faculty of Civil Technology and Architecture
University of Split
Matice Hrvatske 15, Split, 21000, CROATIA
e-mail: sivelic@gradst.hr
$^4$Faculty of Textile Technology
University of Zagreb
Prilaz Baruna Filipovic, 30, Zagreb, 10000, CROATIA
e-mail: pecaric@element.hr


Abstract. In this paper we present results involving positive linear functionals which generalize results that refine the Hadamard inequality. We also present refinements of results proved for Jensen's inequality and introduce new means of Cauchy's type using converses of Jensen's inequality for superquadratic functions.

Received: March 26, 2011

AMS Subject Classification: 26D15

Key Words and Phrases: convex functions, Hermite-Hadamard inequalities, superquadratic functions, Cauchy means, monotonicity

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 1