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

Papers by W S Cheung

Research paper thumbnail of Width-integrals and affine surface area of convex bodies

Banach Journal of Mathematical Analysis, 2008

The main purposes of this paper are to establish some new Brunn-Minkowski inequalities for width-... more The main purposes of this paper are to establish some new Brunn-Minkowski inequalities for width-integrals of mixed projection bodies and affine surface area of mixed bodies, together with their inverse forms.

Research paper thumbnail of Onp-quermassintegral differences function

Proceedings of the Indian Academy of Sciences. Section A, Physical Sciences, May 1, 2006

In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassinte... more In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassintegral differences of convex bodies. Further, we give Minkowski inequality and Brunn-Minkowski inequality for quermassintegral differences of mixed projection bodies.

Research paper thumbnail of Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities

Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities

Springer optimization and its applications, 2018

We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is... more We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is introduced, which generalizes the Lp-radial addition and the Lp-harmonic addition to an Orlicz space, respectively. The variational formula for the dual mixed quermassintegrals with respect to the Orlicz radial harmonic addition is proved, and the new Orlicz dual quermassintegrals generalizes the Lp-dual quermassintegrals. The fundamental notions and conclusions of the dual quermassintegrals and the Minkoswki and Brunn-Minkowski inequalities for the dual quermassintegrals are extended to an Orlicz setting. The new Orlicz-Minkowski and Brunn-Minkowski inequalities in special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn-Minkowski inequality, which also imply the Lp-dual Minkowski inequality and Lp-dual Brunn-Minkowski inequality for the dual quermassintegrals. As application, a dual log-Minkowski inequality is proved.

Research paper thumbnail of Advances in Opial’s Type Integral Inequalities

Advances in Opial’s Type Integral Inequalities

Springer eBooks, 2014

Opial’s inequality and its generalizations, extensions and discretizations play a fundamental rol... more Opial’s inequality and its generalizations, extensions and discretizations play a fundamental role in the study of existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations. Over the years, Opial’s type integral inequalities have been receiving non-diminishing attention. In this article, we establish some new Opial’s type integral inequalities which in special cases yield some existing results of Rozanova, Agarwal-Pang, Pachpatte, Das and Agarwal-Sheng, and provide new and handy tools to qualitative as well as quantitative analysis of solutions to differential equations.

Research paper thumbnail of Two-point boundary value problems for first-order nonlinear fuzzy differential equation1

Journal of Intelligent & Fuzzy Systems, 2016

This paper provides some existence results about first-order fuzzy differential equations with tw... more This paper provides some existence results about first-order fuzzy differential equations with two-point boundary value conditions. We firstly study a class of linear fuzzy differential equation, the results are applied to discuss some nonlinear fuzzy boundary value problems. By using contraction mapping principle in complete metric space, we obtain some existence results about first-order nonlinear fuzzy differential equation with boundary value condition x(0) = αx(T ), where α ∈ R.

Research paper thumbnail of Reverse Hilbert's type integral inequalities

Mathematical Inequalities & Applications, 2014

In this paper, we are motivated by some newer Hilbert-Pachpatte inequalities, and that we derive ... more In this paper, we are motivated by some newer Hilbert-Pachpatte inequalities, and that we derive some similar (but reverse) inequalities. Mathematics subject classification (2010): 26D15.

Research paper thumbnail of Reverse Beckenbach-Dresher’s inequality

Journal of Inequalities and Applications, May 7, 2015

In the paper, we establish an inverse of Beckenbach-Dresher's integral inequality, which provides... more In the paper, we establish an inverse of Beckenbach-Dresher's integral inequality, which provides new estimates on inequality of this type.

Research paper thumbnail of On Inverse Hilbert-Type Inequalities

Journal of Inequalities and Applications, 2008

This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield s... more This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield some of the recent results and provide some new estimates on such types of inequalities.

Research paper thumbnail of An Equivalence Form of the Brunn-Minkowski Inequality for Volume Differences

Journal of The Korean Mathematical Society, Nov 30, 2007

Research paper thumbnail of On Reverse Minkowski-Type Inequalities

On Reverse Minkowski-Type Inequalities

Mediterranean Journal of Mathematics, Oct 2, 2014

In this article, we first establish improvements of the classical Pólya-Szegö inequality. As appl... more In this article, we first establish improvements of the classical Pólya-Szegö inequality. As applications, we prove reverse Minkowski-type inequalities for convex and star bodies.

Research paper thumbnail of Higher order conservation laws

Journal of Differential Geometry, 1969

Research paper thumbnail of On improvements of the Rozanova's inequality

Journal of Inequalities and Applications, Aug 18, 2011

In the present paper, we establish some new Rozanova's type integral inequalities involving highe... more In the present paper, we establish some new Rozanova's type integral inequalities involving higher-order partial derivatives. The results in special cases yield some of the interrelated results on Rozanova's inequality and provide new estimates on inequalities of this type. MS (2000) Subject Classifiication: 26D15.

Research paper thumbnail of On some new Hilbert-type inequalities

Mathematica Slovaca, Jan 26, 2011

In the present paper we establish some new inequalities similar to extensions of Hilbert's double... more In the present paper we establish some new inequalities similar to extensions of Hilbert's double-series inequality and give also their integral analogues. Our results provide some new estimates to these types of inequalities.

Research paper thumbnail of On Minkowski's inequality and its application

Journal of Inequalities and Applications, Sep 27, 2011

In the paper, we first give an improvement of Minkowski integral inequality. As an application, w... more In the paper, we first give an improvement of Minkowski integral inequality. As an application, we get new Brunn-Minkowski-type inequalities for dual mixed volumes.

Research paper thumbnail of On the Hermite-Hadamard type inequalities

Journal of Inequalities and Applications, May 7, 2013

In the present paper, we establish some new Hermite-Hadamard type inequalities involving two func... more In the present paper, we establish some new Hermite-Hadamard type inequalities involving two functions. Our results in a special case yield recent results on Hermite-Hadamard type inequalities. MSC: 26D15

Research paper thumbnail of On Multivariate Grüss Inequalities

Journal of Inequalities and Applications, 2008

The main purpose of the present paper is to establish some new Gr üss integral inequalities in n ... more The main purpose of the present paper is to establish some new Gr üss integral inequalities in n independent variables. Our results in special cases yield some of the recent results on Pachpatte's, Mitrinović's, and Ostrowski's inequalities, and provide new estimates on such types of inequalities.

Research paper thumbnail of On <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle style="text-shadow: 0.02em 0.01em 0.04px"><mi>p</mi></mstyle></mrow><annotation encoding="application/x-tex">\pmb{p}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord" style="text-shadow:0.02em 0.01em 0.04px;"><span class="mord mathnormal">p</span></span></span></span></span>-quermassintegral differences function

arXiv (Cornell University), Jul 25, 2006

In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassinte... more In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassintegral differences of convex bodies. Further, we give Minkowski inequality and Brunn-Minkowski inequality for quermassintegral differences of mixed projection bodies.

Research paper thumbnail of C, A variant of Jessen’s inequality and generalized means

C, A variant of Jessen’s inequality and generalized means

Research paper thumbnail of Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions

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 .

Research paper thumbnail of On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications

On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications

Journal of Inequalities and Applications, 2005

Research paper thumbnail of Width-integrals and affine surface area of convex bodies

Banach Journal of Mathematical Analysis, 2008

The main purposes of this paper are to establish some new Brunn-Minkowski inequalities for width-... more The main purposes of this paper are to establish some new Brunn-Minkowski inequalities for width-integrals of mixed projection bodies and affine surface area of mixed bodies, together with their inverse forms.

Research paper thumbnail of Onp-quermassintegral differences function

Proceedings of the Indian Academy of Sciences. Section A, Physical Sciences, May 1, 2006

In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassinte... more In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassintegral differences of convex bodies. Further, we give Minkowski inequality and Brunn-Minkowski inequality for quermassintegral differences of mixed projection bodies.

Research paper thumbnail of Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities

Orlicz Dual Brunn-Minkowski Theory: Addition, Dual Quermassintegrals, and Inequalities

Springer optimization and its applications, 2018

We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is... more We further consider the Orlicz dual Brunn-Minkowski theory. An Orlicz radial harmonic addition is introduced, which generalizes the Lp-radial addition and the Lp-harmonic addition to an Orlicz space, respectively. The variational formula for the dual mixed quermassintegrals with respect to the Orlicz radial harmonic addition is proved, and the new Orlicz dual quermassintegrals generalizes the Lp-dual quermassintegrals. The fundamental notions and conclusions of the dual quermassintegrals and the Minkoswki and Brunn-Minkowski inequalities for the dual quermassintegrals are extended to an Orlicz setting. The new Orlicz-Minkowski and Brunn-Minkowski inequalities in special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn-Minkowski inequality, which also imply the Lp-dual Minkowski inequality and Lp-dual Brunn-Minkowski inequality for the dual quermassintegrals. As application, a dual log-Minkowski inequality is proved.

Research paper thumbnail of Advances in Opial’s Type Integral Inequalities

Advances in Opial’s Type Integral Inequalities

Springer eBooks, 2014

Opial’s inequality and its generalizations, extensions and discretizations play a fundamental rol... more Opial’s inequality and its generalizations, extensions and discretizations play a fundamental role in the study of existence and uniqueness of initial and boundary value problems for ordinary and partial differential equations as well as difference equations. Over the years, Opial’s type integral inequalities have been receiving non-diminishing attention. In this article, we establish some new Opial’s type integral inequalities which in special cases yield some existing results of Rozanova, Agarwal-Pang, Pachpatte, Das and Agarwal-Sheng, and provide new and handy tools to qualitative as well as quantitative analysis of solutions to differential equations.

Research paper thumbnail of Two-point boundary value problems for first-order nonlinear fuzzy differential equation1

Journal of Intelligent & Fuzzy Systems, 2016

This paper provides some existence results about first-order fuzzy differential equations with tw... more This paper provides some existence results about first-order fuzzy differential equations with two-point boundary value conditions. We firstly study a class of linear fuzzy differential equation, the results are applied to discuss some nonlinear fuzzy boundary value problems. By using contraction mapping principle in complete metric space, we obtain some existence results about first-order nonlinear fuzzy differential equation with boundary value condition x(0) = αx(T ), where α ∈ R.

Research paper thumbnail of Reverse Hilbert's type integral inequalities

Mathematical Inequalities & Applications, 2014

In this paper, we are motivated by some newer Hilbert-Pachpatte inequalities, and that we derive ... more In this paper, we are motivated by some newer Hilbert-Pachpatte inequalities, and that we derive some similar (but reverse) inequalities. Mathematics subject classification (2010): 26D15.

Research paper thumbnail of Reverse Beckenbach-Dresher’s inequality

Journal of Inequalities and Applications, May 7, 2015

In the paper, we establish an inverse of Beckenbach-Dresher's integral inequality, which provides... more In the paper, we establish an inverse of Beckenbach-Dresher's integral inequality, which provides new estimates on inequality of this type.

Research paper thumbnail of On Inverse Hilbert-Type Inequalities

Journal of Inequalities and Applications, 2008

This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield s... more This paper deals with new inverse-type Hilbert inequalities. Our results in special cases yield some of the recent results and provide some new estimates on such types of inequalities.

Research paper thumbnail of An Equivalence Form of the Brunn-Minkowski Inequality for Volume Differences

Journal of The Korean Mathematical Society, Nov 30, 2007

Research paper thumbnail of On Reverse Minkowski-Type Inequalities

On Reverse Minkowski-Type Inequalities

Mediterranean Journal of Mathematics, Oct 2, 2014

In this article, we first establish improvements of the classical Pólya-Szegö inequality. As appl... more In this article, we first establish improvements of the classical Pólya-Szegö inequality. As applications, we prove reverse Minkowski-type inequalities for convex and star bodies.

Research paper thumbnail of Higher order conservation laws

Journal of Differential Geometry, 1969

Research paper thumbnail of On improvements of the Rozanova's inequality

Journal of Inequalities and Applications, Aug 18, 2011

In the present paper, we establish some new Rozanova's type integral inequalities involving highe... more In the present paper, we establish some new Rozanova's type integral inequalities involving higher-order partial derivatives. The results in special cases yield some of the interrelated results on Rozanova's inequality and provide new estimates on inequalities of this type. MS (2000) Subject Classifiication: 26D15.

Research paper thumbnail of On some new Hilbert-type inequalities

Mathematica Slovaca, Jan 26, 2011

In the present paper we establish some new inequalities similar to extensions of Hilbert's double... more In the present paper we establish some new inequalities similar to extensions of Hilbert's double-series inequality and give also their integral analogues. Our results provide some new estimates to these types of inequalities.

Research paper thumbnail of On Minkowski's inequality and its application

Journal of Inequalities and Applications, Sep 27, 2011

In the paper, we first give an improvement of Minkowski integral inequality. As an application, w... more In the paper, we first give an improvement of Minkowski integral inequality. As an application, we get new Brunn-Minkowski-type inequalities for dual mixed volumes.

Research paper thumbnail of On the Hermite-Hadamard type inequalities

Journal of Inequalities and Applications, May 7, 2013

In the present paper, we establish some new Hermite-Hadamard type inequalities involving two func... more In the present paper, we establish some new Hermite-Hadamard type inequalities involving two functions. Our results in a special case yield recent results on Hermite-Hadamard type inequalities. MSC: 26D15

Research paper thumbnail of On Multivariate Grüss Inequalities

Journal of Inequalities and Applications, 2008

The main purpose of the present paper is to establish some new Gr üss integral inequalities in n ... more The main purpose of the present paper is to establish some new Gr üss integral inequalities in n independent variables. Our results in special cases yield some of the recent results on Pachpatte's, Mitrinović's, and Ostrowski's inequalities, and provide new estimates on such types of inequalities.

Research paper thumbnail of On <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle style="text-shadow: 0.02em 0.01em 0.04px"><mi>p</mi></mstyle></mrow><annotation encoding="application/x-tex">\pmb{p}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord" style="text-shadow:0.02em 0.01em 0.04px;"><span class="mord mathnormal">p</span></span></span></span></span>-quermassintegral differences function

arXiv (Cornell University), Jul 25, 2006

In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassinte... more In this paper we establish Minkowski inequality and Brunn-Minkowski inequality for p-quermassintegral differences of convex bodies. Further, we give Minkowski inequality and Brunn-Minkowski inequality for quermassintegral differences of mixed projection bodies.

Research paper thumbnail of C, A variant of Jessen’s inequality and generalized means

C, A variant of Jessen’s inequality and generalized means

Research paper thumbnail of Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions

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 .

Research paper thumbnail of On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications

On certain new Gronwall-Ou-Iang type integral inequalities in two variables and their applications

Journal of Inequalities and Applications, 2005