Huygens inequality

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August undefined, 2024

Web2 mei 2011 · We prove various new trigonometric and hyperbolic inequalities of Jordan, Wilker, Huygens or Cusa-Huygens type. Connections with bivariate means, as well as … Web11 mrt. 2024 · In this paper, we establish some general integral inequalities involving strictly monotone functions. Next, some special cases are discussed. In particular, several estimates of trigonometric and hyperbolic functions are deduced. For instance, we show that Mitrinović-Adamović inequality, Lazarevic inequality, and Cusa-Huygens inequality …

106.19 Some observations on inequalities related to Huygens’ …

Web30 apr. 2024 · The Cusa-Huygens inequality [ 14, 18] is one of the celebrated inequalities in the theory of analytic inequalities involving trigonometric functions. It is stated as … Web1 jan. 2024 · Some new estimates of precision of Cusa–Huygens and Huygens approximations. Preprint arxiv:1907.00712 (2024) Mitrinović, D.S.: Analytic Inequalities. … molly noble

New refinements of Becker-Stark and Cusa-Huygens inequalities …

WebOn Huygens' Inequalities and the Theory of Means Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2012, Article ID 597490, 9 pages doi:10.1155/2012/597490 Research Article On Huygens窶・Inequalities and the Theory of Means Jozsef Sﾂｴ andorﾂｴ Web27 jun. 2024 · 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. Expand. 106. PDF. View 1 excerpt, references methods; Save. http://www.acta.sapientia.ro/acta-math/C4-2/math42-4.pdf hyundai tucson uk owners manual

On the Cusa–Huygens inequality SpringerLink

Some new inequalities of the Huygens type - ScienceDirect

WebThe existing mathematical historical data (see [ 1, 2, 3, 4, 5, 6, 7, 8 ]) show that the above inequality (2) was discovered by Nicolaus De Cusa (1401–1464) using a geometrical method in 1451 and was later in 1664 confirmed by Christian Huygens (1629–1695) when considering the estimation of . Web1 mrt. 2014 · Wilker and Huygens- type inequalities for the generalized trigonometric functions. In this section we shall establish a few Wilker and Huygens- type inequalities for the generalized trigonometric functions. Our first result reads as follows. Theorem 3.1. Let λ, μ > 0. Then (3.1) 1 < λ λ + μ sin p x x r + μ λ + μ tan p x x s, 0 < x < a p ... hyundai tucson trim levels explainedWeb22 jul. 2024 · The famous Huygens inequality for trigonometric functions states that for any 0 < x < p 2 one has 2 sin x x + tan x > 3 (1) while the Wilker inequality asserts that sin x x 2 + tan x x > 2. (2) In [1], S.-H. Wu and H. M. Srivastava established the following inequality, which is sometime known as the second Wilker inequality: 2 x hyundai tucson uk specs

"Web30 apr. 2015 · In this article we present a method for proving a class of inequalities of the form (1). The method is based on the precise approximations of the sine and cosine functions by Maclaurin polynomials of given order. By using this method we present new proofs of some inequalities of C.-P. Chen, W.-S. Cheung [J. Inequal. Appl. 2012:72 … " - Huygens inequality

Huygens inequality

Free Full-Text New Inequalities of Cusa–Huygens Type - MDPI

Web13 dec. 2024 · Homepage / Articles / A SIMPLE PROOF FOR HUYGENS' INEQUALITY. Search for: Recent Posts. INTEGRAL INEQUALITY-476; MINIMUM PROBLEM-98; … Web22 jun. 2024 · 106.19 Some observations on inequalities related to Huygens’ inequality Published online by Cambridge University Press: 22 June 2024 Nick Lord Article Metrics …

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http://files.ele-math.com/abstracts/mia-14-46-abs.pdf WebThe Wilker and Huygens type inequalities (2.1), (2.2), (2.3) and (2.4) have attracted much interest of many mathematicians and have motivated a large number of research papers …

WebChristiaan Huygens FRS Huygens by Caspar Netscher (1671), Museum Boerhaave, Leiden Born (1629-04-14) 14 April 1629 The Hague, Dutch Republic Died 8 July 1695 (1695-07-08) (aged 66) The Hague, Dutch Republic Alma mater University of Leiden University of Angers Known for List Aerial telescope Balance spring Birefringence … Web15 jan. 2024 · We examine Wilker and Huygens-type inequalities involving trigonometric functions making use of results derived in Part I. The Papenfuss–Bach inequal Series …

Web22 nov. 2024 · refinements and sharpness of the Huygens- and Wilker- type inequalities, proof of the second conjecture by Chen and Chueng Citation: Ling Zhu, Zhengjie Sun. … Web15 mrt. 2014 · The natural approach of Wilker–Cusa–Huygens inequalities Math Inequal Appl. (2011) E. Neuman On Wilker and Huygens type inequalities Math. Inequal. Appl. (2012) E. Neuman et al. On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa–Huygens, Wilker and Huygens inequalities Math. …

Webinequality: (4) tgx+sinx > 2x We note that Huygen‘s inequality (2) is stronger that (4) , as (5) tgx+sinx 2 > 2sinx+tgx 3 > x where the ﬁrst relation is equivalent to tgx > sinx. The aim …

WebHuygens type inequalities. Hyperbolic versions will be pointed out, too. 1 Introduction In recent years the trigonometric inequality sinx x < cosx+2 3, 0 < x < π 2 (1) among with … hyundai tucson ultimate hybrid 2021Web15 jan. 2024 · We examine Wilker and Huygens-type inequalities involving trigonometric functions making use of results derived in Part I. The Papenfuss–Bach inequality representing upper and lower bounds for the function x \sec ^ {2}x - \tan x for 0 \le x < \pi /2 is also investigated. hyundai tucson ultimate hybrid 230WebIn this note, we analyze the monotonicity of certain classes of functions related with the Cusa-Huygens inequality, and propose some open problems in this direction. View. hyundai tucson ultimate hybrid 2023WebIn the last two decades, the refinements of the inequalities involving trigonometric and hyperbolic functions such as Wilker type inequalities and Huygens type inequalities have been... hyundai tucson ultimate phevWeb5 mei 2014 · In these papers authors refine the inequalities of trigonometric and hyperbolic functions such as Adamovic-Mitrinovic inequality, Cusa-Huygens inequality, Lazarevic inequality, Huygens inequality, Jordan's inequality, Carlson's inequality, Wilker's inequality, Redheffer's inequality, Wilker-Anglesio inequality, Becker-Stark … hyundai tucson uk delivery timeWeb2 mrt. 2024 · For more about the Wilker type inequality and Huygens type inequalities, the reader may see [6–13]. In this paper, we establish some new Wilker and Cusa type inequalities for the generalized trigonometric and hyperbolic functions. Some known inequalities in are the special cases of our results. hyundai tucson turbo chargerWeb22 nov. 2024 · refinements and sharpness of the Huygens- and Wilker- type inequalities, proof of the second conjecture by Chen and Chueng Citation: Ling Zhu, Zhengjie Sun. Refinements of Huygens- and Wilker- type inequalities [J]. AIMS Mathematics, 2024, 5 (4): 2967-2978. doi: 10.3934/math.2024241 Related Papers: Reader Comments your … hyundai tucson turbo review