Affiliation:
1. School of Mathematics, Hangzhou Normal University, Hangzhou, China
2. Department of Mathematics, Huzhou University, Huzhou, China
Abstract
In this paper, we provide a systematic way to study on some general Wilker-Huygens type inequalities for the trigonometric and hyperbolic functions,
lemniscate and hyperbolic lemniscate functions, and their corresponding
inverse functions. Our results are some extensions and refinements of the
recently published results in [A. Mhanna, On a general Huygens-Wilker
inequality, Appl. Math. E.-Notes, 20 (2020), 79-81; MR4076436], and improve
many previous results involving Wilker-Huygens type inequalities.
Publisher
National Library of Serbia
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference46 articles.
1. G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen: Conformal Invariants, Inequalities, and Quasiconformal Maps. John Wiley & Sons, New York, (1997).
2. J. M. Borwein and P. B. Borwein: Pi and the AGM. A study in analytic number theory and computational complexity, Wiley, New York, (1998).
3. B. C. Carlson: Algorithms involving arithmetic and geometric means, Amer. Math. Mon. 78 (1971), 496-505.
4. C.-P. Chen and W.-S. Cheung: Inequalities and solution to Oppenheim's problem, Integral Transforms Spec. Funct. 23(5) (2012), 325-336.
5. C.-P. Chen and W.-S. Cheung: Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012): 72.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Frame’s Types of Inequalities and Stratification;Cubo (Temuco);2024-03-19
2. Sharp double-exponent type bounds for the lemniscate sine function;Applicable Analysis and Discrete Mathematics;2024
3. Sharp bounds for the lemniscatic mean by the weighted Hölder mean;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2023-04-06