For a,b>0 with aξ =b, we define
M_{p}=M^{1/p}(a^{p},b^{p})\text{if}p\neq 0 \text{and} M_{0}=\sqrt{ab}, where
M=A,He,L,I,P,T,N,Z and Y stand for the arithmetic mean, Heronian mean,
logarithmic mean, identric (exponential) mean, the first Seiffert mean, the
second Seiffert mean, Neuman-S\'{a}ndor mean, power-exponential mean and
exponential-geometric mean, respectively. Generally, if M is a mean of a
and b, then Mpβ is also, and call "power-type mean". We prove the
power-type means Ppβ, Tpβ, Npβ, Zpβ are increasing in p on
R and establish sharp inequalities among power-type means Apβ,
Hepβ, Lpβ, Ipβ, Ppβ, Npβ, Zpβ, Ypβ% . From this a
very nice chain of inequalities for these means
L_{2}<P<N_{1/2}<He<A_{2/3}<I<Z_{1/3}<Y_{1/2} follows. Lastly, a conjecture is
proposed.Comment: 11 page