Title of article :
A GENERALIZATION OF JORDAN’S INEQUALITY AND AN APPLICATION
Author/Authors :
Huo, Zhen-Hong Zhongyuan University of Technology - College of Science, China , Niu, Da-Wei Zhongyuan University of Technology - College of Information and Business, China , Cao, Jian Hangzhou Normal University - Department of Mathematics, China , Qi, Feng Tianjin Polytechnic University - College of Science - Department of Mathematics, China
Abstract :
In this article, a new generalization of Jordan’s inequality ∑n,k=1 μk(θt − xt)^k ≤sin x/x−sinθ/θ≤∑n,k=1(θt − xt)^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 refined.
Keywords :
Jordan’s inequality , Yang’s inequality , L’Hˆospital’s rule , Refinement , Application
Journal title :
Hacettepe Journal Of Mathematics and Statistics
Journal title :
Hacettepe Journal Of Mathematics and Statistics
