Journal ArticleDOI
Wilker- and Huygens-type inequalities and solution to Oppenheim's problem
Chao-Ping Chen,Wing-Sum Cheung +1 more
TLDR
This paper established Wilker-and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions and provided a laconic proof to Oppenheim's problem associated with inequalities involving the sine and cosine functions.Abstract:
We establish Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions. We also provide a laconic proof to Oppenheim’s problem associated with inequalities involving the sine and cosine functions.read more
Citations
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Journal ArticleDOI
Sharp Wilker- and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions
TL;DR: In this article, sharp Wilker and Huygens-type inequalities for inverse trigonometric and inverse hyperbolic functions were established for both functions, and they were shown to be equivalent to the following:
Journal ArticleDOI
Sharpness of Wilker and Huygens type inequalities
Chao-Ping Chen,Wing-Sum Cheung +1 more
TL;DR: The authors presented an elementary proof of Wilker's inequality involving trigonometric functions, and established sharp Wilker and Huygens type inequalities for trigonometrical functions with respect to trigonometry.
Journal ArticleDOI
Inequality chains for Wilker, Huygens and Lazarević type inequalities
Chao-Ping Chen,József Sándor +1 more
TL;DR: In this paper, various refinements of inequalities related to the Wilker, Huygens, or Lazarevic inequalities are presented, including a modification of the Lévy inequalities.
Journal ArticleDOI
Sharp inequalities of Mitrinovic–Adamovic type
TL;DR: In this article, sharp Mitrinovic-Adamovic type inequalities for circular functions are established, and the analogue one of Lazarevic-type inequalities for hyperbolic functions is proved by a simple method.
Journal ArticleDOI
A proof of two conjectures of Chao-Ping Chen for inverse trigonometric functions
TL;DR: In this article, the authors proved two conjectures stated by Chao-Ping Chen in [Int. Trans. Spec. Funct. 23:12 (2012), 865--873] using a method for proving inequalities of mixed trigonometric polynomial functions.
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
On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
Edward Neuman,József Sándor +1 more
TL;DR: This paper showed that Wilker's inequality, Huygens' inequality, and some other related inequalities all follow from the Cusa-Huyhens inequality and a generalization of the latter result is also obtained.
Journal ArticleDOI
The natural approach of Wilker-Cusa-Huygens inequalities
TL;DR: This new approach of Wilker-Cusa-Huygens inequalities permits us to give new proofs then to refine much these inequalities and the authors are convinced that it is suitable to establish many other similar inequalities.
Related Papers (5)
On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities
Edward Neuman,József Sándor +1 more