International Journal of Mathematics and Mathematical Sciences (Jan 2012)
A Nice Separation of Some Seiffert-Type Means by Power Means
Abstract
Seiffert has defined two well-known trigonometric means denoted by π« and π―. In a similar way it was defined by Carlson the logarithmic mean β as a hyperbolic mean. Neuman and SΓ‘ndor completed the list of such means by another hyperbolic mean β³. There are more known inequalities between the means π«,π―, and β and some power means ππ. We add to these inequalities two new results obtaining the following nice chain of inequalities π0<β<π1/2<π«<π1<β³<π3/2<π―<π2, where the power means are evenly spaced with respect to their order.
