| Abstrakt: |
Let P(a,b) and T(a,b) be the first and second Seiffert's means for two positive numbers a and b, in this paper, for any fixed p ∈ R, we present the optimal parameters, αp, βp, γp, μp ∈ [0,1] such that the inequalities Hp(a,b; αp) ≤ P(a,b) ≤ Hp(a,b; βp), Hp(a,b; λp) ≤ T(a,b) ≤ Hp(a,b; μp) hold true for all a,b > 0, where Hp(a,b; ω) is the weighted p-order Hölder (power) mean with the weightω ω∈ [0,1]. As applications, various sharp inequalities for P(a,b) and T(a,b), including the sharp power mean bounds, will be established. [ABSTRACT FROM AUTHOR] |
