SOME INTEGRAL INEQUALITIES IN N INDEPENDENT VARIABLES

ＳＯＭＥＩＮＴＥＧＲＡＬＩＮＥＱＵＡＬＩＴＩＥＳＩＮＮＩＮＤＥＰＥＮＤＥＮＴＶＡＲＩＡＢＬＥＳＹＡＮＧＥＮＨＡＯ（杨恩浩）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｔｃｓ，ＪｉｎａｎＵｎｉｖｅｒｓｉｔｙ，Ｇｎａｎｇｚｈｏｕ５１Ｏ６３２，Ｃｈｉｎａ）Ａ...     

Some integral and discrete inequalities in several independent variables

We improve the constants in some integral and discrete inequalities in n independent variables which are due to Agarwal and Sheng [1] and Agarwal and Pang [2].     

Some generalized integral inequalities and their applications

In this paper, we generalize some integral inequalities to more general situations. We establish bounds on the solutions and, by means of examples, we show the usefulness of our results in investigating the global existence of the solutions of integral equations and differential equations.     

关于n个独立变元的欧阳型非线性积分不等式

讨论R^n上的Ou-Iang型非线性积分不等式，所得结论是杨恩浩的R^1上的Ou-Iang型非线性积分不等式的自然推广和改进。     

On quadratic integral inequalities of the second order

The aim of this paper is to generalize the uniform method of obtaining integral inequalities in order to derive inequalities involving a function h, its first and second derivatives with weights. Such inequalities have been considered before by others, but other methods were applied. Our method makes it possible to obtain, in a natural way, the equality conditions important in differential equations. Moreover it allows us to avoid some assumptions on weights that have to be given in other methods. Then the inequality will be examined in order to simplify the boundary conditions for h. These considerations will be followed by examples with Chebyshev weight functions and constant weights with the classical Hardy, Littlewood, Polya inequality as a special case.     

含有n个无关变元的欧阳型非线性离散不等式

讨论N^n上的Ou—Iang型离散不等式，得到了几个非线性离散不等式．并将所得结论用于研究一类非线性时滞偏差分方程解的有界性．     

Some Hardy type integral inequalities

We present new kinds of Hardy integral inequalities involving some generalization and improvement.     

Bellman-Bihari integral inequalities in several independent variables

In this paper we unify certain types of integral inequalities which are established by Bellman, Bihari, Deo and Dhongade.     

On retarded integral inequalities and their applications

The main results of [J. Math. Anal. Appl. 285 (2003) 436-443] are here generalized to the following retarded integral inequalities:

     

Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations

Some new weakly singular integral inequalities of Gronwall-Bellman type are established, which generalized some known weakly singular inequalities and can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. Some applications to fractional differential and integral equations are also indicated.     

On some new integral inequalities of Gronwall-Bellman-Pachpatte type

In this paper, we establish new nonlinear integral inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used as handy tools to study the qualitative as well as the quantitative properties of solutions of some nonlinear ordinary differential and integral equations. The purpose of this paper is to extend certain results which proved by Pachpatte in [Inequalities for Differential and Integral Equations, Academic Press, New York and London, 1998]. Some applications are also given to illustrate the usefulness of our results.     

Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay

In this paper, we generalize some integral inequalities to more general situations, and the inequalities of Pachpatte type are corollaries of our's. We establish bounds on the solutions, and we show the usefulness of our results in investigating the asymptotic behavior and the stability on the solutions of integral equations, differential equations and integro-differential equations with time delay.     

Lebesgue-stieltjes integral inequalities in several variables with retardation

The aim of this paper is to establish some new Lebesgue-Stieltjes integral inequalities inn independent variables with retardation which generalize and unify continuous and discrete inequalities of the Gronwall-Bellman-Bihari type inn independent variables.     

On some fundamental integral inequalities in two independent variables

The present paper obtains two independent variable generalizations of the integral inequalities of Gollwitzer, Langenhop, and Pachpatte. The bounds provided by these inequalities are adequate in many applications in the theory of partial differential and integral equations.     

Some integral inequalities for logarithmically convex functions

The main aim of the present note is to establish new Hadamard like integral inequalities involving log-convex function. We also prove some Hadamard-type inequalities, and applications to the special means are given.     

On some discrete inequalities in two independent variables

In this paper we establish some new nonlinear difference inequalities. We also present an application of one inequality to certain nonlinear sum-difference equation.     

Some new Gronwall-Bellman-Bihari type integral inequalities with delay

Some new linear and nonlinear delay integral inequalities of G-B-B type are obtained which generalize some results of O. Akinyele [1], P. Ch. Tsamatos and S. K. Ntouyas [16]. Application examples are also given. This revised version was published online in June 2006 with corrections to the Cover Date.     

Henry-Gronwall type retarded integral inequalities and their applications to fractional differential equations with delay

This paper presents retarded integral inequalities of Henry-Gronwall type. Applying these inequalities, we study certain properties of solutions to fractional differential equations with delay.