Sharpening Jordan's inequality and the Yang Le inequality
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The following inequality is established: sin x x ≤ 2 π + π −2 π 3 ( π 2 − 4 x 2 ) , x ∈ ( 0, π / 2 ] is established and an application of this inequality gives an improvement of the Yang Le inequality.About:
This article is published in Applied Mathematics Letters.The article was published on 2006-03-01 and is currently open access. It has received 52 citations till now.read more
Citations
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Journal ArticleDOI
Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems
Feng Qi,Da-Wei Niu,Bai-Ni Guo +2 more
TL;DR: A survey and expository article on Jordan's inequality and related problems can be found in this paper. But it is not a comprehensive survey of all the applications of Jordan's inequalities.
Journal ArticleDOI
Monotonicity criterion for the quotient of power series with applications
TL;DR: In this paper, the necessary and sufficient condition for monotonicity of the quotient of power series is presented, and some gaps and misquotations in certain published articles are pointed out and corrected, while some known results involving the Landen inequalities for zero-balanced hypergeometric functions are improved.
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On Jordan type inequalities for hyperbolic functions
TL;DR: Lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved in this paper for trigonometric and hyperbolic functions with respect to the Jordan inequality.
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On Jordan type inequalities for hyperbolic functions
TL;DR: Lower and upper bounds for the Jordan inequality for trigonometric and hyperbolic functions have been proved in this article for functions such as and, and their generalizations have also been proved.
Journal ArticleDOI
A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality, II
Shanhe Wu,Lokenath Debnath +1 more
TL;DR: A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality.
References
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Book
Conformal Invariants, Inequalities, and Quasiconformal Maps
TL;DR: In this paper, the Gr/tzsch ring capacity estimates for the Gr /tzsch Ring Constant Bounds for Distortion Functions in the Plane are derived for quadruples and quasiconformal mappings.
Journal ArticleDOI
Generalized elliptic integrals and modular equations
TL;DR: In geometric function theory, generalized elliptic integrals and functions arise from the Schwarz-Christoffel transformation of the upper half-plane onto a parallelogram and are naturally related to Gaussian hypergeometric functions.
Journal ArticleDOI
New strengthened Jordan's inequality and its applications
Lokenath Debnath,Chang-Jian Zhao +1 more
TL;DR: The main purpose of the present article is to strengthen Jordan's inequality by improving some new results proved by Zhao.
Related Papers (5)
A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality, II
Shanhe Wu,Lokenath Debnath +1 more