This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integ...This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.展开更多
In this paper, by introducing three parameters a, b and λ, we give some new generalizations of Hardy-Hilbert’s integral inequality. As applications, we con-sider its equivalent form and some particular results.
Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with t...Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results are considered.展开更多
In this paper, by introducing the norm ｜｜x｜｜ （x ∈ Rn）, a multiple Hardy- Hilbert＇s integral inequality with the best constant factor and it＇s equivalent form are given.
In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is pro...In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is proved to be the best possible.And then some important and especial results are enumerated.As applications,some equivalent forms are given.展开更多
In this paper,a new reverse extended Hardy＇s integral inequality is proved by means of weight coefficients and the technique of real analysis.Some particular results are considered.
A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some applica...A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.展开更多
In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function...In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function.展开更多
In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.
Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also der...Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.展开更多
In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional ...In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.展开更多
In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.
In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which gi...In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.展开更多
Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) i...Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) is the maximal function on R+n+1, which was introduced by Ruiz,F. and Torrea, J.展开更多
In this paper,a new integral inequality is established by an elementary inequality and a generalization of this new integral inequality,and its application is presented.
We establish explicit bounds on some more general retarded integral inequalities which can be used as convenient tools in some applications,and give some examples which show the feasibility of our results.
Some new inequalities of Hermite-Hadamard's integration are established. As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3], a ne...Some new inequalities of Hermite-Hadamard's integration are established. As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3], a new upper bound is given. Under special conditions,the bound is smaller than that in [3].展开更多
Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, so...Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.展开更多
基金supported by the National Natural Science Foundation of China(61473070,61433004,61627809)SAPI Fundamental Research Funds(2013ZCX01,2013ZCX14)
文摘This paper investigates the stability of time-delay systems via a multiple integral approach. Based on the refined Jensen-based inequality, a novel multiple integral inequality is proposed. Applying the multiple integral inequality to estimate the derivative of Lyapunov-Krasovskii functional(LKF) with multiple integral terms, a novel stability condition is formulated for the linear time-delay systems. Two numerical examples are employed to demonstrate the improvements of our results.
基金Foundation item:The NSF (0177) of Guangdong Institutions of Higher Learning,College and University
文摘In this paper, by introducing three parameters a, b and λ, we give some new generalizations of Hardy-Hilbert’s integral inequality. As applications, we con-sider its equivalent form and some particular results.
基金Project supported by the Natural Science Foundation of the Institutions of Higher Learning of Guangdong Province (GrantNo.05Z026)the Natural Science Foundation of Guangdong Province (Grant No.7004344)
文摘Through using weight function, we give a new Hilbert-type integral inequality with two independent parameters and two pair of conjugate exponents, which is a best extension of a Hilbert-type integral inequality with the homogeneous kernel of 0-degree. The equivalent form, the reverses and some particular results are considered.
文摘In this paper, by introducing the norm ｜｜x｜｜ （x ∈ Rn）, a multiple Hardy- Hilbert＇s integral inequality with the best constant factor and it＇s equivalent form are given.
基金Supported by the Project of Scientific Research Fund of Hunan Provincial Education Department (GrantNo.09C789)
文摘In this paper it is shown that a new Hilbert-type integral inequality can be established by introducing two parameters m（m ∈ N） and λ（λ 0）.And the constant factor expressed by the Bernoulli number and π is proved to be the best possible.And then some important and especial results are enumerated.As applications,some equivalent forms are given.
基金Supported by the Natural Science Foundation of Guangdong Province (Grant No.70043344)
文摘In this paper,a new reverse extended Hardy＇s integral inequality is proved by means of weight coefficients and the technique of real analysis.Some particular results are considered.
基金the Natural Science Foundation of Guangdong Pronvincial.
文摘A new integral inequality with power nonlinearity is obtained,which generalizes some extensions of L. Ou-Iang's inequality given by B.G. Pachpatte. Discrete analogy of the new integral inequality and some application examples are also indicated.
基金The Key Scientific and Technological Innovation Team Project(2014KCT-15)in Shaanxi Province
文摘In this article, we extend some estimates of the right-hand side of the Hermite-Hadamard type inequality for preinvex functions with fractional integral.The notion of logarithmically s-Godunova-Levin-preinvex function in second sense is introduced and then a new Herrnite-Hadarnard inequality is derived for the class of logarithmically s-Godunova-Levin-preinvex function.
文摘In this note,by introudcing a couple of parameters T,t and estimating the weight function effectively,Hilberts integral inequalities are well generalized. As applications,we give some new Hilbers type inequalities.
基金Supported by the Natural Science Foundation of Guangdong Pronvince( 0 1 1 471 ) and Education Bu-reau( 0 1 76)
文摘Some new inequalities involving improper integrals are established in the paper which generalize the related results due to Pachpatte and Rodrigues.Discrete analogues of the integral inequalities obtained are also derived.An example is given to show that the bound in Theorem 1 is not improvable.
文摘In this paper, first we obtain some new fractional integral inequalities. Then using these inequalities and fixed point theorems, we prove the existence of solutions for two different classes of functional fractional differential equations.
基金supported by the National Natural Science Foundation of China(No.60974025)
文摘In this paper,a nonlinear integral inequality in n independent variables with retardation is established,the result obtained generalizes and improves some previous results.
文摘In this article, we study the reverse HSlder type inequality and HSlder inequality in two dimensional case on time scales. We also obtain many integral inequalities by using HSlder inequalities on time scales which give Hardy＇s inequalities as spacial cases.
文摘Let μ be a measure on the upper half-space R+n+1,and v a weight on Rn,we give a characterization for the pair (v,μ) such that ||μ(fv)||L(μ)≤c||f||L(μ)where is an N-function satisfying Δ2 condition and uf(x,t) is the maximal function on R+n+1, which was introduced by Ruiz,F. and Torrea, J.
基金supported by the National Natural Science Foundation of China(No.60674020)
文摘In this paper,a new integral inequality is established by an elementary inequality and a generalization of this new integral inequality,and its application is presented.
基金supported by the National Natural Sciences Foundation of China(10771118)Natural Sciences Foundation of Shandong Province(ZR2009AM011 and ZR2009AQ010)
文摘We establish explicit bounds on some more general retarded integral inequalities which can be used as convenient tools in some applications,and give some examples which show the feasibility of our results.
基金Supported by the Key Scientific and Technological Innovation Team Project in Shaanxi Province(2014KCT-15)
文摘Some new inequalities of Hermite-Hadamard's integration are established. As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3], a new upper bound is given. Under special conditions,the bound is smaller than that in [3].
基金The project is supported in part by the NSF of Guangdong Province (Grnat No. 940651) the SF of Key Discipline of the State Council Office of Overseas Chinese Affairs of China (Grant No.93-93-6)
文摘Nonlinear integral and discrete inequalities are obtained. which are related to some recent results of B. C. Pachpatte in [1] given therein as generalizations of Ou-Iang’s integral inequality[2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered.
