In the present paper, we first prove the logarithmic convexity of the elementary function b x −a x x , where x 6= 0 and b > a > 0. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.

In this paper, we find the greatest values [Formula: see text] and the smallest values [Formula: see text] such that the double inequalities [Formula: see text] and [Formula: see text] hold for all [Formula: see text] with [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the arithmetic-geometric, Toader and generalized logarithmic means of two posi...

and Applied Analysis 3 Alzer and Qiu 27 found the sharp bound of 1/2 L a, b I a, b in terms of the power mean as follows: Mc a, b < 1 2 L a, b I a, b 1.8 for all a, b > 0 with a/ b, with the best possible parameter c log 2/ 1 log 2 . The main purpose of this paper is to find the least value λ ∈ 0, 1 and the greatest value p p α such that αH a, b 1 − α L a, b > Mp a, b for α ∈ λ, 1 and all a, b ...

Correspondence should be addressed to Mustapha Raı̈ssouli, raissouli [email protected] Received 4 December 2010; Accepted 9 February 2011 Academic Editor: B. N. Mandal Copyright q 2011 Mustapha Raı̈ssouli. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work ...

A class of games for finding a leader among a group of candidates is studied in detail. This class covers games based on coin-tossing and rock-paper-scissors as special cases and its complexity exhibits similar stochastic behaviors: either of logarithmic mean and bounded variance or of exponential mean and exponential variance. Many applications are also discussed.

Sharp bounds for the Neuman-Sándor mean and for the logarithmic mean are established. The bounding quantities are the one-parameter bivariate means called the p-means. In this paper best values of the parameters of the bounding means are obtained. Mathematics subject classification (2010): 26E60, 26D07, 26D20.

BACKGROUND AND PURPOSE Diffusion-weighted imaging (DWI) and perfusion MRI were used to examine the spatiotemporal evolution of stroke lesions in adult macaques with ischemic occlusion. METHODS Permanent MCA occlusion was induced with silk sutures through an interventional approach via the femoral artery in adult rhesus monkeys (n = 8, 10-21 years old). The stroke lesions were examined with hi...