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.
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.
The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the bas...The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.展开更多
The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit fun...The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.展开更多
In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o...This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.展开更多
In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve ...The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.展开更多
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as ...In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.展开更多
In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
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 article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
The main result of this paper is presented as follows Let h is homogeneous and symmetric of degree and Then where provided the integrals on the RHS do exists. Some other special cases are also
Given two positive constantsαandβ,we prove that the integral inequality∫_0~1 f^(α+β)(x)dx≥∫_0~1 f~α(x)x~βdx holds for all non-negative valued continuous functions f satisfying∫_x^1 f(t)dt≥∫_x^1 tdt for x∈...Given two positive constantsαandβ,we prove that the integral inequality∫_0~1 f^(α+β)(x)dx≥∫_0~1 f~α(x)x~βdx holds for all non-negative valued continuous functions f satisfying∫_x^1 f(t)dt≥∫_x^1 tdt for x∈[0,1]if and only ifα+β≥1.This solves an open problem proposed recently by Ngo,Thang,Dat,and Tuan.展开更多
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
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 Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamar...Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.展开更多
In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,...In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,Φ_2 are Young functions, w_i(i = 1,2,3, 4) are weights, f~* =sup n≥0 |f_n| and f_∞=lim n→∞ f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.展开更多
For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= (y1, Y2,…, ym) and 7 denotes the m-tuple (f1, f2,…, fm). In this note, the one- weighted and ...For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= (y1, Y2,…, ym) and 7 denotes the m-tuple (f1, f2,…, fm). In this note, the one- weighted and two-weighted boundedness on Lp (JRn) space for multilinear fractional integral operator I(am) and the fractional multi-sublinear maximal operator Mα(m) are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα(m).展开更多
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.
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.
文摘The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.
基金The project supported by the National Natural Science Foundation of China(19891180)Doctorate Foundation of Xi'an Jiaotong University
文摘The Bueckner work conjugate integrals are studied for cracks in anisotropic clastic solids.The difficulties in separating Lekhnitskii's two complex arguments involved in the integrals are overcome and explicit functional representa- tions of the integrals are given for several typical cases.It is found that the pseudo- orthogonal property of the eigenfunction expansion forms presented previously for isotropic cases,isotropic bimaterials,and orthotropic cases,are proved to be also valid in the present case of anisotropic material.Finally,Some useful path-independent in- tegrals and weight functions are proposed.
文摘In this paper, we establish several inequalities for some differantiable mappings that are connected with the Riemann-Liouville fractional integrals. The analysis used in the proofs is fairly elementary.
基金Supported by the National Natural Science Foundation of China (10771054,11071200)the NFS of Fujian Province of China (No. 2010J01013)
文摘This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained.
文摘In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
文摘The main aim of this present note is to establish three new Hermite-Hadamard type integral inequalities for r-convex functions. The three new Hermite-Hadamard type integral inequalities for r-convex functions improve the result of original one by H?lder’s integral inequality, Stolarsky mean and convexity of function.
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
文摘In this paper, by introducing some parameters and estimating the weight coefficient, we give a new Hilbert’s inequality with the integral in whole plane and with a non-homogeneous and the equivalent form is given as well. The best constant factor is calculated by the way of Complex Analysis.
文摘In this paper we show that a log-convex function satisfies Hadamard's inequality, as well as we give an extension for this result in several directions.
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 article, we obtain the LP-boundedness of commutators of Lipschitz functions and singular integrals with non-smooth kernels on Euclidean spaces.
文摘The main result of this paper is presented as follows Let h is homogeneous and symmetric of degree and Then where provided the integrals on the RHS do exists. Some other special cases are also
文摘Given two positive constantsαandβ,we prove that the integral inequality∫_0~1 f^(α+β)(x)dx≥∫_0~1 f~α(x)x~βdx holds for all non-negative valued continuous functions f satisfying∫_x^1 f(t)dt≥∫_x^1 tdt for x∈[0,1]if and only ifα+β≥1.This solves an open problem proposed recently by Ngo,Thang,Dat,and Tuan.
基金supported by the Natural Science Foundation of China(11701176,61673169,11301127,11626101,11601485)the Science and Technology Research Program of Zhejiang Educational Committee(Y201635325)
文摘We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
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 key scientific and technological innovation team project in shaanxi province(2014KCT-15)the Foundations of Shaanxi Educational committee(NO.18Jk0152)
文摘Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.
基金Supported by the National Natural Science Foundation of China(11871195)
文摘In this article, some necessary and sufficient conditions are shown in order that weighted inequality of the form ■holds a.e. for uniformly integrable martingales f =(f_n)n≥0 with some constant C > 0,where Φ_1,Φ_2 are Young functions, w_i(i = 1,2,3, 4) are weights, f~* =sup n≥0 |f_n| and f_∞=lim n→∞ f_n a.e. As an application, two-weight weak type maximal inequalities of martingales are considered, and particularly a new equivalence condition is presented.
基金the NNSF of China under Grant#10771110NSF of Ningbo City under Grant#2006A610090
文摘For 0 〈 α 〈 mn and nonnegative integers n ≥ 2, m≥ 1, the multilinear fractional integral is defined bywhere →y= (y1, Y2,…, ym) and 7 denotes the m-tuple (f1, f2,…, fm). In this note, the one- weighted and two-weighted boundedness on Lp (JRn) space for multilinear fractional integral operator I(am) and the fractional multi-sublinear maximal operator Mα(m) are established re- spectively. The authors also obtain two-weighted weak type estimate for the operator Mα(m).