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New Refinements and Improvements of Jordan’s Inequality

by Lina Zhang 1 and Xuesi Ma 2,*
1
School of Computer Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China
2
School of Mathematic and Information Science, Henan Polytechnic University, Jiaozuo 454000, China
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 284; https://doi.org/10.3390/math6120284
Received: 8 November 2018 / Revised: 20 November 2018 / Accepted: 21 November 2018 / Published: 26 November 2018
The polynomial bounds of Jordan’s inequality, especially the cubic and quartic polynomial bounds, have been studied and improved in a lot of the literature; however, the linear and quadratic polynomial bounds can not be improved very much. In this paper, new refinements and improvements of Jordan’s inequality are given. We present new lower bounds and upper bounds for strengthened Jordan’s inequality using polynomials of degrees 1 and 2. Our bounds are tighter than the previous results of polynomials of degrees 1 and 2. More importantly, we give new improvements of Jordan’s inequality using polynomials of degree 5, which can achieve much tighter bounds than those previous methods. View Full-Text
Keywords: Jordan’s inequality; polynomial; bound Jordan’s inequality; polynomial; bound
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Zhang, L.; Ma, X. New Refinements and Improvements of Jordan’s Inequality. Mathematics 2018, 6, 284.

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