[PDF] Top 20 Three Inequalities Involving Hyperbolically Trigonometric Functions

... The study of Jordan’s and Kober’s inequality and inequalities of trigonometric functions has a rich literature, for example, [1, 2, 4, 6, 7, 8, 9, 10, 11] and references therein. There are many ... See full document

... Inequalities involving trigonometric and inverse trigonometric functions play an impor- tant role and have many applications in science and engineering [2, 8, 12, 17–19, ... See full document

... Proof Inequalities (.)-(.) easily follow by the elementary differential method, and we omit all details here. Inequality (.) can be derived from a well-known inequality given in [, p.]) by Adamović and ... See full document

... All three parameters are functions of the distribution’s terminal ...hypergeometric functions depend on terminal and initial ...hypergeometric functions which appear in its left-hand ... See full document

... Algorithms involving arithmetic and geometric ...lemniscate functions and lemniscatic ...Two-sided inequalities for the lemniscate ...lemniscate functions and lemniscatic mean ... See full document

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

... These inequalities were of great interest throughout the research, since they were ex- tended in different forms in the recent ...these inequalities have also practical importance, because they provide some ... See full document

... two inequalities relating to Bernoulli’s and Euler’s numbers and power series expansions of cotangent function, secant function, cosecant function and logarithms of functions involving sine function, ... See full document

... type inequalities (1) and (2) have attracted much interest of many mathemati- cians and have motivated a large number of research papers involving different proofs and various generalizations and ... 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 ... 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

... Hermite-Hadamard inequalities and other integral inequalities involving two functions in ...ties involving two functions in R  ... See full document

... In this paper we establish some inequalities of Hadamard’s type involving Godunova-Levin functions, P-functions, quasi-convex functions, J- quasi-convex functions, Wright-convex function[r] ... See full document

... FINK, Inequalities Involving Functions and their Integrals and Derivatives, Kluwer Academic Publishers, Dordrecht, 1991.. [10] D.S.[r] ... See full document

... symmetric functions can be expressed by the Hardy function (see [] and Remark ), and that the interpolating quasi- polynomial can be expressed by the generalized Vandermonde determinant (see [, ]), the Hardy ... See full document

... To the best of authors’ knowledge, only some fractional q-integral inequalities have been established in recent years. That is, only Öğünmez and Özkan [], Bohner and Ferreira [] and Yang [] obtained some ... See full document

... There have been a lot of literature about these two double inequalities and their history, background, refinements, extensions, generalizations and applications. For more information, please refer to [5, 7, 9, 10, ... See full document

... where x, y ∈ J and λ ∈ [, ]; see []. Many properties of P-class functions can be found in [–]. Note that the set of all P-class functions contains all convex functions and also all nonnegative ... See full document

... integral equations involving first kind Bessel functions of different orders and a particular weight function to dual integral equations with trigonometric sine function as kernels in cl[r] ... See full document

... type inequalities involv- ing two convex and log-convex functions, ...type inequalities for products of two m-convex and (α, m)-convex ...s-convex functions were proved by Kırmacı, Bakula, ¨ ... See full document