[PDF] Top 20 20. Optimal inequalities for hyperbolic and trigonometric functions

... years inequalities involving trigonometric and hyperbolic inequalities have attracted attention of several ...Wilker inequalities for trigonometric and hyperbolic func- ... See full document

... In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity ... See full document

... three inequalities for the cosine function, hyper- bolic sine function and hyperbolic cosine function, which are similar to Redheffer’s inequality (3), are ... See full document

... the trigonometric integrals, we have in this paper finding a series of power, some of trigonometric functions that did not exist before in the first ...of trigonometric functions with ... See full document

... new inequalities and improv- ing certain ...remarkable inequalities involving inverse trigonometric functions, we show that the new inequalities presented in this paper are more refined ... See full document

... Functions (.) and (.) can be found (see [], Chapter , [], p. and [–]). Another pair of lemniscate functions, the arc lemniscate tangent arctl and the hyperbolic arc lemniscate tangent ... See full document

... classical inequalities for generalized trigonometric and hyperbolic func- tions, such as Mitrinović–Adamović inequality, Huygens’ inequality, and Wilker’s inequal- ity, were ...type ... See full document

... new inequalities of the Huygens type for trigonometric and hyperbolic ...that inequalities (1) and (3) are simple consequences of the arithmetic-geometric mean inequality together with the ... See full document

... Abstract. Inequalities involving trigonometric and hyperbolic functions are ...of inequalities proved by Adamovi´ c and Mitrinovi´ c, Cusa, Huygens, Lazarevi´ c and ... See full document

... 40 G. D. Anderson, M. K. Vamanamurthy, and M. Vuorinen, “Topics in special functions,” in Papers on Analysis: A Volume Dedicated to Olli Martio on the Occasion of His 60th Birthday, J. Heinonen, T. Kilpel¨ainen, ... See full document

... 11. Wu, S-H: On extension and refinement of Wilker’s inequality. Rocky Mt. J. Math. 39(2), 683-687 (2009) 12. Wu, S-H, Debnath, L: Wilker-type inequalities for hyperbolic functions. Appl. Math. Lett. ... See full document

... In this paper we, respectively, give simple proofs of some remarkable trigonometric inequalities, based on the Padé approximation method. We also obtain rational refinements of these inequalities. We ... See full document

... Many inequalities of these type and their refinements have been proved in [1-16] and the ref- erences ...the functions mentioned above and to improve the bounds of ... See full document

... many functions which are not one-one, onto or both and hence we can not talk of their ...that trigonometric functions are not one-one and onto over their natural domains and ranges and hence their ... See full document

... 3 Main results In this section, we present several Lazarević and Cusa type inequalities involving the hyperbolic sine and cosine functions with two parameters.... From Proposition ., w[r] ... See full document

... of hyperbolic functions called hyperbolic Fibonacci functions replacing the discrete variable n in equation () with the continuous variable x that takes its values from the set of real ... See full document

... Have you ever wondered why there are 90° in a right angle? This is actually part of a sexagesimal system, based on the number 60. This number system originated over 4000 years ago with the ancient Sumerians and was ... See full document

... As a consequence, we get some new sharp estimates to various classical inequalities concerning the gamma function and hyperbolic functions.... Acknowledgements This paper is supported by[r] ... See full document

... In this paper, we provide alternative proofs to some results pro- posed in the article ”New inequalities involving circular, inverse circu- lar, hyperbolic, inverse hyperbolic and expone[r] ... See full document

... new inequalities which reveal the further relationship between the inverse tangent function arctan x and the inverse hyperbolic sine function sinh –1 ...inverse hyperbolic tangent and inverse ... See full document