W S Cheung - Academia.edu (original) (raw)

Papers by W S Cheung

Journal of Inequalities and Applications, Aug 18, 2011

Mathematica Slovaca, Jan 26, 2011

Journal of Inequalities and Applications, Sep 27, 2011

Journal of Inequalities and Applications, May 7, 2013

Journal of Inequalities and Applications, 2008

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arXiv (Cornell University), Jul 25, 2006

Filomat, 2014

In this article, we establish several properties of the composition of functions which are relate... more In this article, we establish several properties of the composition of functions which are related to certain classes of completely monotonic functions and logarithmically completely monotonic functions. 1. Introduction, Preliminaries and the Main Results Throughout this paper, we denote by N the set of all positive integers, N 0 := N ∪ {0} and R + := (0, ∞). Furthermore, I + is an open interval contained in R + , I o is the interior of the interval I ⊂ R, R is the set of all real numbers, R(f) denotes the range of the function f and C(I) is the class of all continuous functions on the interval I. We first recall some definitions which we shall use and some basic results which are related to them. Definition A (see [27]). A function f is said to be absolutely monotonic on an interval I, if f ∈ C(I) has derivatives of all orders on I o and f (n) (x) 0 (x ∈ I o) for all n ∈ N 0. The class of all absolutely monotonic functions on I is denoted by AM(I). Definition B (see [27]). A function f is said to be completely monotonic on an interval I, if f ∈ C(I) has derivatives of all orders on I o and (−1) n f (n) (x) 0 (x ∈ I o) for all n ∈ N 0 .

Journal of Inequalities and Applications, 2005

Journal of Inequalities and Applications, 2009

Applied Mathematics and Computation, 2013

We study the recent investigations on a class of functions which are logarithmically completely m... more We study the recent investigations on a class of functions which are logarithmically completely monotonic. Two open problems are also presented.

Chapman and Hall/CRC eBooks, Apr 29, 2005

In this paper, we establish some new discrete Gronwall-Bellman-Ou-Iang type inequalities over 2-d... more In this paper, we establish some new discrete Gronwall-Bellman-Ou-Iang type inequalities over 2-dimensional lattices. These, on one hand, generalize some existing results in the literature and on the other hand, provide a handy tool for the study of qualitative properties of solutions of difference equations. We illustrate this by applying these new results to certain boundary value problem for difference equations.

Boundary Value Problems, 2011

Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral dif... more Existence and Lyapunov stability of periodic solutions for a generalized higher-order neutral differential equation are established.

Proceedings of the American Mathematical Society, Mar 1, 1993

In this paper some new integral inequalities of the Poincare type, on a region of rectangular dim... more In this paper some new integral inequalities of the Poincare type, on a region of rectangular dimensions, involving many functions in many variables are obtained. These in turn can be used to serve as generators of other integral inequalities.

Mathematical Inequalities & Applications, 1998

In this paper some new Wirtinger-type integral inequalities involving many functions of many vari... more In this paper some new Wirtinger-type integral inequalities involving many functions of many variables are established. These on the one hand improve existing results in the subject concerned and on the other hand can serve as generators of other integral inequalities of such type.

International Journal of Mathematics and Mathematical Sciences, 2005

A double inequality involving the constant e is proved by using an inequality between the logarit... more A double inequality involving the constant e is proved by using an inequality between the logarithmic mean and arithmetic mean. As an application, we generalize the weighted Carleman-type inequality. n 1/Λn < e ∞ n=1 λ n a n .

Mathematical Inequalities & Applications, 2005

This is a continuation of an earlier work of Cheung-Pečarić. By using the C-technique developed b... more This is a continuation of an earlier work of Cheung-Pečarić. By using the C-technique developed by Cheung and Pečarić, some new and interesting Hardy-type inequalities involving vector-valued functions are established. These generalize and imporve some known results by Cheung, Cheung-Hanjš-Pečarić, Izumi-Izumi, and Pachpatte.

Taiwanese Journal of Mathematics, Mar 1, 2007