TY - JOUR
A2 - Neuman, Edward
AU - Costin, Iulia
AU - Toader, Gheorghe
PY - 2012
DA - 2012/07/03
TI - A Nice Separation of Some Seiffert-Type Means by Power Means
SP - 430692
VL - 2012
AB - Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯. In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are more known inequalities between the means 𝒫, 𝒯, and ℒ and some power means 𝒜p. We add to these inequalities two new results obtaining the following nice chain of inequalities 𝒜0<ℒ<𝒜1/2<𝒫<𝒜1<ℳ<𝒜3/2<𝒯<𝒜2, where the power means are evenly spaced with respect to their order.
SN - 0161-1712
UR - https://doi.org/10.1155/2012/430692
DO - 10.1155/2012/430692
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi Publishing Corporation
KW -
ER -