A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fra...A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.展开更多
Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In ...Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.展开更多
Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a...Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.展开更多
This paper focuses on the design problem of a memoryless state feedback robust H-infinity controller for a class of uncertain neutral systems. By using a newly established integral inequality, a new delay-dependent bo...This paper focuses on the design problem of a memoryless state feedback robust H-infinity controller for a class of uncertain neutral systems. By using a newly established integral inequality, a new delay-dependent bounded real lemma for such systems is derived without involving a fixed model transformation. Furthermore, new delay-dependent sufficient conditions for the existence of robust H-infinity controllers are presented in terms of nonlinear matrix inequalities. A design procedure involving an iterative algorithm is also proposed to design such controllers. Numerical examples are given to demonstrate the less conservatism of the proposed method.展开更多
Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted...Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.展开更多
By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particul...By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particular results.展开更多
In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the or...In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the original.展开更多
In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.
In this paper,we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is c...In this paper,we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales.Those results generalize the recent results of Gan Shixin [2].展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11801342)the Natural Science Foundation of Shaanxi Province(Grant No.2023-JC-YB-043).
文摘A new concept generalized(h,m)−preinvex function on Yang’s fractal sets is proposed.Some Ostrowski’s type inequalities with two parameters for generalized(h,m)−preinvex function are established,where three local fractional inequalities involving generalized midpoint type,trapezoid type and Simpson type are derived as consequences.Furthermore,as some applications,special means inequalities and numerical quadratures for local fractional integrals are discussed.
基金Supported by the Natural Science Foundation of China(10671117)Supported by the Science Foundation of China Three Gorges University
文摘Lutwak proved the Brunn-Minkowski inequality for the quermassintegrals of Fiery Lρ-combination. Wang and Leng gave the Brunn-Minkowski inequality for the dual quermassintegrals of Lρ-harmonic radial combination. In the paper, we establish the isolate forms of the Brunn-Minkowski inequality for quermassintegrals and dual quermassintegrals,respectively.
文摘Within the framework of Orlicz Brunn-Minkowski theory recently introduced by Lutwak, Yang, and Zhang [20, 21], Gardner, Hug, and Weil [5, 6] et al, the dual harmonic quermassintegrals of star bodies are studied, and a new Orlicz Brunn-Minkowski type inequality is proved for these geometric quantities.
基金the National Natural Science Foundation of China (No. 60525304)
文摘This paper focuses on the design problem of a memoryless state feedback robust H-infinity controller for a class of uncertain neutral systems. By using a newly established integral inequality, a new delay-dependent bounded real lemma for such systems is derived without involving a fixed model transformation. Furthermore, new delay-dependent sufficient conditions for the existence of robust H-infinity controllers are presented in terms of nonlinear matrix inequalities. A design procedure involving an iterative algorithm is also proposed to design such controllers. Numerical examples are given to demonstrate the less conservatism of the proposed method.
基金supported by the Key Project of Gansu Provincial National Science Foundation(23JRRA1022)the National Natural Science Foundation of China(12071431)+1 种基金the Fundamental Research Funds for the Central Universities(lzujbky-2021-ey18)the Innovative Groups of Basic Research in Gansu Province(22JR5RA391).
文摘Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.
文摘By introducing some parameters and estimating the weight function,we obtain an extension of reverse Hilbert-type inequality with the best constant factor.As applications,we build its equivalent forms and some particular results.
文摘In [1], the authors established the Brunn-Minkowski inequality for centroid body. In this paper, we give an isolate form and volume difference of it, respectively. Both of these results are strength versions of the original.
基金supported by the National Natural Science Foundation of China(No.11201232)Qing Lan Project of Jiangsu Province
文摘In this paper we establish the oscillation inequality of harmonic functions and HOlder estimate of the functions in the domain of the Laplacian on connected post critically finite （p.c.f.） self-similar sets.
基金Supported by the Youth Foundation of the Department of Education of Sichuan Province（07ZB042） Supported by Natural Science Foundation of the Department of Education of Sichuan Province（09ZC071）
文摘In this paper,we establish the Hàjek-Rèniy type inequality for Banach space valued martingales generalizing the recent results of Tómcs and L'ibor [1].Then p-uniformly smoothable Banach space is characterized in terms of the Hàjek-Rèniy type inequality for Banach space valued martingales.Those results generalize the recent results of Gan Shixin [2].
