IJPAM: Volume 23, No. 3 (2005)

RADO AND POPOVICIU TYPE INEQUALITIES FOR
PSEUDO ARITHMETIC AND GEOMETRIC MEANS

Vasile Mihesan
Department of Mathematics
Technical University of Cluj-Napoca
15, C. Daicoviciu Str., Cluj-Napoca, 400020, ROMANIA
e-mail: Vasile.Mihesan@math.utcluj.ro


Abstract.In this paper we prove Rado and Popoviciu type inequalities for pseudo arithmetic and geometric means $a_n$ and $g_n$, defined by

\begin{displaymath}a_n=\frac{P_n}{p_1}-\frac{1}{p_1}\sum_{i=2}^np_ix_i\ \ \mbox{and}\ \ g_n=x_1^{P_n/p_1} / \prod_{i=2}^nx_i^{p_i/p_1},\end{displaymath}

where $x_i$ and $p_i$ $(i=1,2,\dots,n)$ are positive real number and $P_n=\sum\limits_{i=1}^np_i$.

Received: May 10, 2005

AMS Subject Classification: 26D15, 26E60

Key Words and Phrases: pseudo arithmetic and geometric means, inequalities

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 23
Issue: 3