A Generalization of Jordan's Inequality and an Application  ABSTRACT  |  FULL TEXT

Year 2011, Volume: 40 Issue: 1, 53 - 61, 01.01.2011

Zh.-h. Huo D.-w. Niu J. Cao  f. Qi Feng Qi

Abstract

In this article, a new generalization of Jordan’s inequality
Xn
k=1
µk

θ
t − x
t
k ≤
sin x
x
−
sin θ
θ
≤
Xn
k=1
ωk

θ
t − x
t
k
for t ≥ 2, n ∈ N and θ ∈ (0, π] is established, where the coefficients µk
and ωk are defined by recursion formulas, and are the best possible. As
an application, Yang’s inequality is refine

Keywords

ds: Jordan’s inequali, Yang’s inequali

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