A Generalization of Jordan’s Inequality and an Application
نویسندگان
چکیده
In this article, a new generalization of Jordan’s inequality n ∑ k=1 μk ( θ − x )k ≤ sinx x − sin θ θ ≤ n ∑ k=1 ωk ( θ − x )k for t ≥ 2, n ∈ N and θ ∈ (0, π] is established, where the coefficients μk and ωk defined by recursion formulas (11) and (12) are the best possible. As an application, Yang’s inequality is refined.
منابع مشابه
A General Generalization of Jordan’s Inequality and a Refinement of L. Yang’s Inequality
In this article, for t ≥ 2, a general generalization of Jordan’s inequality Pn k=1 μk θt − xt k ≤ sin x x − sin θ θ ≤nk=1 ωk θt − xt k for n ∈ N and θ ∈ (0, π] is established, where the coefficients μk and ωk defined by recursing formulas (11) and (12) are the best possible. As an application, L. Yang’s inequality is refined.
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