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SOME INEQUALITIES OF HERMITE-HADAMARD TYPE FOR s-CONVEX FUNCTIONS 被引量:9
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作者 Mohammad W. Alomari Maslina Darus Ugur S. Kirmaci 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1643-1652,共10页
In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.
关键词 convex function s-convex function Hadamard’s inequality
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Integral Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>s</i>-Convex 被引量:4
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作者 Ling Chun Feng Qi 《Applied Mathematics》 2012年第11期1680-1685,共6页
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.
关键词 INTEGRAL inequALITY Hermite-Hadamard’s INTEGRAL inequALITY s-Convex Function Derivative Mean
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A Class of the Geometric Inequalities Involving k-Brocard Distance 被引量:5
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作者 WEN Jia-jin KE Rui LUE Tao 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2006年第2期210-219,共10页
Let P be an inner point of a convex N-gon ΓN : A1A2… ANA1(N ≥ 3), and let di,k denote the distance from the point Ai+k to the line PAi(i = 1,2,…,N, Ai = Aj〈=〉 i ≡ j(modN)), which is called the k-Brocard... Let P be an inner point of a convex N-gon ΓN : A1A2… ANA1(N ≥ 3), and let di,k denote the distance from the point Ai+k to the line PAi(i = 1,2,…,N, Ai = Aj〈=〉 i ≡ j(modN)), which is called the k-Brocard distance for P of ΓN. We have proved the following double-inequality: If P ∈ ΓN, k = N↑∩i=1∠Ai-kAiAi+k(1 ≤ k 〈 N/2,i =1,2,…,N), and r ≤ lnN-ln(N-1)/ln2+2[lnN-ln(N-1)], then (1/N N↑∑↑i=1di^r, k)^1/r≤1/N coskπ/N N↑∑↑i=1|AiAi+k|≤sin2kπ/2sinπ/N(1/N N↑∑↑i=1|AiAi+1|^2. 展开更多
关键词 convex N-gon k-Brocard distance Hoelder inequality Janous-Klamkin's conjecture
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Davis's Inequalities for Two-Parameter Banach Space Valued Strong Martingales and Geometrical Properties of Banach Spaces 被引量:3
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作者 YE Chen GAN Shi xin ZHANG Feng 《Wuhan University Journal of Natural Sciences》 CAS 2000年第2期131-136,共6页
In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach sp... In this paper we investigated theL 1 norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces. 展开更多
关键词 two parameterB valued strong martingale Daviss inequality p smoothable q convexifiable
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Some integral inequalities on time scales 被引量:1
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作者 Adnan Tuna Servet Kutukcu 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第1期23-29,共7页
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
关键词 integral inequalities Hoelder's inequalities Hardy's inequalities time scales reverse inequality
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SINGLE PROJECTION ALGORITHM FOR VARIATIONAL INEQUALITIES IN BANACH SPACES WITH APPLICATION TO CONTACT PROBLEM 被引量:3
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作者 Yekini SHEHU 《Acta Mathematica Scientia》 SCIE CSCD 2020年第4期1045-1063,共19页
We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach space.The underline cost function of the variational inequality is assumed to be monotone a... We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach space.The underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous.A weak convergence result is obtained under reasonable assumptions on the variable step-sizes.We also give the strong convergence result for when the underline cost function is strongly monotone and Lipchitz continuous.For this strong convergence case,the proposed method does not require prior knowledge of the modulus of strong monotonicity and the Lipschitz constant of the cost function as input parameters,rather,the variable step-sizes are diminishing and non-summable.The asymptotic estimate of the convergence rate for the strong convergence case is also given.For completeness,we give another strong convergence result using the idea of Halpern iteration when the cost function is monotone and Lipschitz continuous and the variable step-sizes are bounded by the inverse of the Lipschitz constant of the cost function.Finally,we give an example of a contact problem where our proposed method can be applied. 展开更多
关键词 variational inequality 2-uniformly convex Banach space Tseng’s algorithm strong convergence rate of convergence
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ON CRITICAL CASES OF SOBOLEV'S INEQUALITIES FOR HEISENBERG GROUPS 被引量:1
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作者 杨乔华 《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1584-1592,共9页
We prove some Trudinger-type inequalities and Brezis-Gallouet-Wainger inequality on the Heisenberg group, extending to this context the Euclidean results by T. Ozawa.
关键词 sobolev's inequality Brezis-Gallouet-Wainger inequality Heisenberg group
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DOOB’S MAXIMAL INEQUALITIES FOR MARTINGALES IN VARIABLE LEBESGUE SPACE 被引量:1
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作者 Peide LIU 《Acta Mathematica Scientia》 SCIE CSCD 2021年第1期283-296,共14页
In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditio... In this paper we deal with the martingales in variable Lebesgue space over a probability space.We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space.The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent.In particular,we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities.Finally,we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p>1. 展开更多
关键词 variable Lebesgue space martingale inequality norm convergence Doob’s maximal inequality
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Hermite-Hadamard Type Fractional Integral Inequalities for Preinvex Functions 被引量:1
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作者 lian tie-yan tang wei +1 位作者 zhou rui ji you-qing 《Communications in Mathematical Research》 CSCD 2018年第4期351-362,共12页
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
关键词 Hermite-Hadamard's integral inequality Riemann-Liouville fractional integral Holder's integral inequality
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Several Hermite-Hadamard Type Inequalities for Harmonically Convex Functions in the Second Sense with Applications 被引量:1
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作者 Wang Wen Yang Shi-guo Liu Xue-ying 《Communications in Mathematical Research》 CSCD 2016年第2期105-110,共6页
In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Final... In this paper, we first introduce the concept "harmonically convex functions" in the second sense and establish several Hermite-Hadamard type inequalities for harmonically convex functions in the second sense. Finally, some applications to special mean are shown. 展开更多
关键词 Hermite-Hadamard's inequality harmonically convex function mean inequality
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Inequalities relating to L_p-version of Petty's conjectured projection inequality 被引量:1
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作者 王卫东 冷岗松 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第2期269-276,共8页
Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequalit... Petty's conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty's conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty's conjectured projection inequality and the Lp-Petty projection inequality are given, respectively. 展开更多
关键词 Lp-version Petty projection inequality Petty's conjectured projectioninequality Lp-projection body REVERsE
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Some Inequalities of Hermite-Hadamard Type for Functions Whose 3rd Derivatives Are <i>P</i>-Convex 被引量:1
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作者 Boyan Xi Shuhong Wang Feng Qi 《Applied Mathematics》 2012年第12期1898-1902,共5页
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose 3rd derivatives are P-convex.
关键词 INTEGRAL inequALITY Hermite-Hadamard’s INTEGRAL inequALITY P-Convex Function Derivative
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CONVEX CONCENTRATION INEQUALITIES FOR CONTINUOUS GAS AND STOCHASTIC DOMINATION 被引量:1
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作者 马宇韬 《Acta Mathematica Scientia》 SCIE CSCD 2009年第5期1461-1468,共8页
In this article, we consider the continuous gas in a bounded domain ∧ of R^+ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity... In this article, we consider the continuous gas in a bounded domain ∧ of R^+ or R^d described by a Gibbsian probability measure μη∧ associated with a pair interaction φ, the inverse temperature β, the activity z 〉 0, and the boundary condition η. Define F ∫ωf(s)wA(ds). Applying the generalized Ito's formula for forward-backward martingales (see Klein et M. [5]), we obtain convex concentration inequalities for F with respect to the Gibbs measure μη∧. On the other hand, by FKG inequality on the Poisson space, we also give a new simple argument for the stochastic domination for the Gibbs measure. 展开更多
关键词 continuous gas Gibbs measure convex concentration inequality Ito's formula stochastic domination
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Dresher's Type Inequalities for Dual Quermassintegral 被引量:1
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作者 WEI Bo WANG Wei-dong 《Chinese Quarterly Journal of Mathematics》 2015年第2期199-205,共7页
In this paper, we establish two Dresher's type inequalities for dual quermassintegral with Lp-radial Minkowski linear combination and Lp-harmonic Blaschke linear combination, respectively. Our results in special c... In this paper, we establish two Dresher's type inequalities for dual quermassintegral with Lp-radial Minkowski linear combination and Lp-harmonic Blaschke linear combination, respectively. Our results in special cases yield some new dual Lp-Brunn-Minkowski inequalities for dual quermassintegral. 展开更多
关键词 star bodies Dresher’s inequality Lp-Brunn-Minkowski inequality
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STRONG CONVERGENCE OF AN INERTIAL EXTRAGRADIENT METHOD WITH AN ADAPTIVE NONDECREASING STEP SIZE FOR SOLVING VARIATIONAL INEQUALITIES 被引量:1
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作者 Nguyen Xuan LINH Duong Viet THONG +2 位作者 Prasit CHOLAMJIAK Pham Anh TUAN Luong Van LONG 《Acta Mathematica Scientia》 SCIE CSCD 2022年第2期795-812,共18页
In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our me... In this work,we investigate a classical pseudomonotone and Lipschitz continuous variational inequality in the setting of Hilbert space,and present a projection-type approximation method for solving this problem.Our method requires only to compute one projection onto the feasible set per iteration and without any linesearch procedure or additional projections as well as does not need to the prior knowledge of the Lipschitz constant and the sequentially weakly continuity of the variational inequality mapping.A strong convergence is established for the proposed method to a solution of a variational inequality problem under certain mild assumptions.Finally,we give some numerical experiments illustrating the performance of the proposed method for variational inequality problems. 展开更多
关键词 Inertial method Tseng’s extragradient viscosity method variational inequality problem pseudomonotone mapping strong convergence
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Fermions: Spin, Hidden Variables, Violation of Bell’s Inequality and Quantum Entanglement
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作者 Doron Kwiat 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第4期1613-1627,共15页
Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s co... Using real fields instead of complex ones, it was recently claimed, that all fermions are made of pairs of coupled fields (strings) with an internal tension related to mutual attraction forces, related to Planck’s constant. Quantum mechanics is described with real fields and real operators. Schrodinger and Dirac equations then are solved. The solution to Dirac equation gives four, real, 2-vectors solutions ψ1=(U1D1)ψ2=(U2D2)ψ3=(U3D3)ψ4=(U4D4)where (ψ1,ψ4) are coupled via linear combinations to yield spin-up and spin-down fermions. Likewise, (ψ2,ψ3) are coupled via linear combinations to represent spin-up and spin-down anti-fermions. For an incoming entangled pair of fermions, the combined solution is Ψin=c1ψ1+c4ψ4where c1and c4are some hidden variables. By applying a magnetic field in +Z and +x the theoretical results of a triple Stern-Gerlach experiment are predicted correctly. Then, by repeating Bell’s and Mermin Gedanken experiment with three magnetic filters σθ, at three different inclination angles θ, the violation of Bell’s inequality is proven. It is shown that all fermions are in a mixed state of spins and the ratio between spin-up to spin-down depends on the hidden variables. 展开更多
关键词 FERMIONs sPIN Hidden Variables Bell’s inequality Violation spin Entanglement
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Generalizations of Hermite-Hadamard Type Inequalities Involving S-convex Functions 被引量:3
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作者 LIAN Tie-yan TANG Wei 《Chinese Quarterly Journal of Mathematics》 2018年第3期278-286,共9页
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
关键词 Hermite-Hadamard's INTEGRAL inequALITY s-convex function Hslder's integralinequality
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An Improvement of the Hardy-Hilbert Type Integral Inequalities and an Application
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作者 HE Le-ping CHEN Xiao-yu SHANG Xiao-zhou 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期68-74,共7页
In this paper, it is shown that Hardy-Hilbert's integral inequality with parameter is improved by means of a sharpening of Hoeder's inequality. A new inequality is established as follows:∫^∞α∫^∞α f(x)g(y)... In this paper, it is shown that Hardy-Hilbert's integral inequality with parameter is improved by means of a sharpening of Hoeder's inequality. A new inequality is established as follows:∫^∞α∫^∞α f(x)g(y)/(x+y+2β)dxdy〈π/sin(π/p){∫^∞α f^p(x)dx}1/p·{∫^∞αgq(x)dx}1/q·(1-R)^m,where R=(Sp (F, h) - Sq (G, h))^2, m= min (1/p, 1/q). As application; an extension of Hardy-Littlewood's inequality is given. 展开更多
关键词 Hardy-Hilbert's type inequality Hardy-Littlewood's inequality Hoelder's inequality beta function
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Vacuum Dependent Bell Local Hidden Variable Models and Generalized C.H.S.H. Inequalities 被引量:1
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作者 Gianpaolo Bei 《Journal of Applied Mathematics and Physics》 2022年第1期11-20,共10页
We extend a previous model of the author which generalizes Bell local hidden variable models to the case of entangled photon pairs assuming that the standard Bell correlation functions depend on a hidden vacuum index.... We extend a previous model of the author which generalizes Bell local hidden variable models to the case of entangled photon pairs assuming that the standard Bell correlation functions depend on a hidden vacuum index. We deduce a generalization of Bell theorem assuming that classical observables are not dichotomic and that photon pair emission and detection is not a stationary stochastic process. We derive a photon imperfect polarization correlation functions due to rotational invariance breaking induced by hidden vacuum spin currents. We implement formally this approach deducing a generalization of C.H.S.H. inequalities which asymptotically converges to the standard one and which might be competitive with standard quantum mechanics predictions. We suggest to test this inequalities conceiving new E.P.R.-Bell like tests with time dependent detector efficiency and photon flux. Finally, we suggest to apply these generalized inequalities to the correlation functions of entangled classical spinning waves realized recently with metamaterials. 展开更多
关键词 Vacuum Index Complex Hidden Variables Vacuum Dependent Photons Imperfect Correlations Vacuum Dependent Detector Efficiency Generalized C.H.s.H. inequalities
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THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS
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作者 张松艳 《Acta Mathematica Scientia》 SCIE CSCD 2010年第3期993-1003,共11页
In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A∨u) - Vu =0, and the three-ball inequalities on the characteristic plane and the three-cyli... In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A∨u) - Vu =0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation Эtu-div(A∨u) + Vu = 0, where the singular potential V belonging to the Kato-Fefferman- Phong's class. Some applications are also discussed. 展开更多
关键词 Three-sphere inequality three-cylinder inequality singular partial differential equation Kato-Fefferman-Phong's class Lipschitz domain
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