Shanhe Wu

A new generalized and sharp version of Jordan’s inequality and its applications to the improvement of the Yang Le inequality, II

Abstract A new generalized and sharp version of Jordan’s inequality is proved and it is applied in the improvement of the Yang Le inequality. Moreover, a mistake in the proof of sharpening Jordan’s inequality due to Zhu [S.H. Wu, On generalizations and refinements of Jordan type inequality, Octogon Math. Mag. 12(1) (2004) 267–272] is corrected.

A weighted and exponential generalization of Wilker's inequality and its applications

In this paper, the authors first prove a weighted and exponential generalization of Wilkers inequality. The main result presented here is then applied with a view to deriving an improved version of the Sándor–Bencze conjectured inequality. Some other closely-related inequalities are also considered.

Hermite–Hadamard type inequalities for harmonically convex functions via fractional integrals

Abstract In this paper, the authors established Hermite–Hadamard’s inequalities for harmonically convex functions via fractional integrals and obtained some Hermite–Hadamard type inequalities of these classes of functions.

A further refinement of Wilker's inequality

By introducing the Taylor polynomials, a significantly refined version of Wilkers inequality is established. The result is then used to obtain several substantially more refined inequalities of the Wilker type.

Inequalities for convex sequences and their applications

Using the theory of majorization, new inequalities for convex sequences are proved. A necessary and sufficient condition for a convex sequence is established. This reveals an important relationship between the convex sequence and the majorized inequality. Finally, some applications of our new inequalities and some improvements of certain known results are presented.

A further refinement of a Jordan type inequality and its application

Abstract By introducing Taylor polynomials, a new sharpened and generalized version of Jordan’s inequality is established. The result is then used to obtain a substantially more refined inequality of Jordan type. Moreover, an application of the results presented here toward the improvement of the Yang Le inequality is also considered in this paper.

Jordan-type inequalities for differentiable functions and their applications

Abstract In this work, we extend Jordan’s inequality to obtain a new type of inequality involving functions and their higher-order derivatives. The result is then used to obtain some higher accurate inequalities of Jordan type.

A generalization of L’Hôspital-type rules for monotonicity and its application

Abstract This paper deals with a generalization of L’Hospital-type rules for monotonicity. The result is then used to establish a class of two-sided bounding inequalities for higher-order differentiable functions. As consequences, some refined upper and lower bounds for exponential function, logarithmic function, trigonometric functions and hyperbolic functions are derived.

Some refined families of Jordan-type inequalities and their applications

Abstract In this paper, the classical Jordans inequality is studied once again, a new sharpened and generalized version of Jordans inequality is given by means of polynomial representation, and the result thus derived is then used to obtain several substantially more refined inequalities of Jordan type. Finally, an application of the results presented in this paper toward the improvement of the Yang Le inequality is considered.

Some improvements and generalizations of Steffensen’s integral inequality

Abstract In this paper, the authors present several interesting results on improvements of Steffensen’s integral inequality. Moreover, an error in a generalization of Steffensen’s inequality due to Mercer [P.R. Mercer, Extensions of Steffensen’s inequality, J. Math. Anal. Appl. 246 (2000) 325–329] is corrected.