Da-Wei Niu

Refinements, Generalizations, and Applications of Jordan's Inequality and Related Problems

This is a survey and expository article. Some new developments on refinements, generalizations, and applications of Jordans inequality and related problems, including some results about Wilker-Anglesios inequality, some estimates for three kinds of complete elliptic integrals, and several inequalities for the remainder of power series expansion of the exponential function, are summarized.

A general refinement of Jordan's inequality and a refinement of L. Yang's inequality

Abstract In the article, a general double refinement of Jordans inequality, for n∈ℕ, is established, where the coefficients α k and β k defined by recursing formulas (9) and (10) are the best possible. As an application, L. Yangs inequality is refined.

FOUR LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTIONS INVOLVING GAMMA FUNCTION

In this paper, two classes of functions, involving a parameter and the Euler gamma function, and two functions, involving the Euler gamma function, are verified to be logarithmically completely monotonic in (-½, ∞) or (0,∞) and an inequality involving the Euler gamma function, due to J.Wendel, is refined partially.

AN EXTENSION AND A REFINEMENT OF VAN DER CORPUT'S INEQUALITY

van der Corputs inequality is extended and refined by using Euler-Maclaurin formula and other analytic techniques.

A Generalization of Van Der Corput's Inequality

In this article, van der Corputs inequality is generalized by using the well known Euler-Maclaurin sum formula and other analytic techniques.

More notes on a functional equation

In this short note, a mathematical proposition on a functional equation for x, y ≠ 0, which is encountered in calculus, is generalized step by step. These steps involve continuity, differentiability, a functional equation, an ordinary differential linear equation of the first order, and relationships between them.

Simplification of Coefficients in Differential Equations Associated with Higher Order Frobenius–Euler Numbers

In the paper, by virtue of the Faà di Bruno formula, some properties of the Bell polynomials of the second kind, and the inversion formulas of binomial numbers and the Stirling numbers of the first and second kinds, the authors simplify meaningfully and significantly coefficients in two families of ordinary differential equations associated with higher order Frobenius–Euler numbers. E-mail addresses: qifeng618@gmail.com, qifeng618@hotmail.com, qifeng618@qq.com, nnddww@gmail.com, bai.ni.guo@gmail.com, bai.ni.guo@hotmail.com. 2010 Mathematics Subject Classification. Primary 34A05; Secondary 05A16, 11A25, 11B37, 11B68, 11B73, 11B83, 33B10, 34A34.