In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the...In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition. We provide some sufficient conditions that ensure the asymptotic stability of the system. Furthermore, we present the construction of a feedback stabilizing controller for conformable fractional bilinear systems.展开更多
In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,...In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.展开更多
In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovsk...In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.展开更多
设T是核满足Dini条件的多线性奇异积分算子,T∗是T的极大算子。T∗b,S是T∗与一类可测函数{bi}∞i=1生成的广义交换子。本文讨论了当{bi}∞i=1属于Lipschitz空间,T∗b,S在Lebesgue 空间的有界性。Let T be an m-linear Calder´on-Zygmu...设T是核满足Dini条件的多线性奇异积分算子,T∗是T的极大算子。T∗b,S是T∗与一类可测函数{bi}∞i=1生成的广义交换子。本文讨论了当{bi}∞i=1属于Lipschitz空间,T∗b,S在Lebesgue 空间的有界性。Let T be an m-linear Calder´on-Zygmund operator with kernel satisfying Dini-type condition, T∗be the maximal operator of T. T∗b,Sis the generalized commutator of T∗ with a class of measurable functions {bi}∞i=1.In this paper, we discuss the boundedness of T∗b,S on Lebesgue spaces when {bi}∞i=1 belongs to Lipschitz spaces.展开更多
本文讨论了p-进域上的奇异积分算子与Lipschitz函数生成的交换子的有界性, 证明了交换子是从Lebesgue空间IJCampanato空间有界的。In this paper, we discussed the boundedness of commutator generated by singular integral operator...本文讨论了p-进域上的奇异积分算子与Lipschitz函数生成的交换子的有界性, 证明了交换子是从Lebesgue空间IJCampanato空间有界的。In this paper, we discussed the boundedness of commutator generated by singular integral operator and Lipschitz function on the p-adic field. We proved that the commutator is bounded from Lebesgue space to certain Campanato space.展开更多
This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the n...This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.展开更多
文摘In this paper, we study the stability of a class of conformable fractional-order systems using the Lyapunov function. We assume that the nonlinear part of the system satisfies the one-sided Lipschitz condition and the quadratic inner-bounded condition. We provide some sufficient conditions that ensure the asymptotic stability of the system. Furthermore, we present the construction of a feedback stabilizing controller for conformable fractional bilinear systems.
基金Supported by the National Natural Science Foundation of China(11671397,11571160,12071052)the Yue Qi Young Scholar of China University of Mining and Technology(Beijing)。
文摘In this paper,the authors study the multilinear commutators generated by a class of multilinear singular integral operators with generalized kernels and Lipschitz functions.By establishing the sharp maximal estimates,the boundedness of this kind of multilinear commutators on product of weighted Lebesgue spaces can be obtained.
基金Supported by Fujian Provincial Natural Science Foundation of China(2024J01792)。
文摘In the present paper,the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined.It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators.The degree of approximation is given by the modulus of continuity.It has been stressed that,there are other operators having the same error estimation with the operators,arising from the Sz´asz-Durrmeyer operators.Then the degree of global approximation is obtained in a special Lipschitz type function space.Further,a Voronovskaja type asymptotic formula and Gr¨uss-Voronovskaja type theorem are given.The approximation with these operators is visualized with the help of error tables and graphical examples.
文摘设T是核满足Dini条件的多线性奇异积分算子,T∗是T的极大算子。T∗b,S是T∗与一类可测函数{bi}∞i=1生成的广义交换子。本文讨论了当{bi}∞i=1属于Lipschitz空间,T∗b,S在Lebesgue 空间的有界性。Let T be an m-linear Calder´on-Zygmund operator with kernel satisfying Dini-type condition, T∗be the maximal operator of T. T∗b,Sis the generalized commutator of T∗ with a class of measurable functions {bi}∞i=1.In this paper, we discuss the boundedness of T∗b,S on Lebesgue spaces when {bi}∞i=1 belongs to Lipschitz spaces.
文摘本文讨论了p-进域上的奇异积分算子与Lipschitz函数生成的交换子的有界性, 证明了交换子是从Lebesgue空间IJCampanato空间有界的。In this paper, we discussed the boundedness of commutator generated by singular integral operator and Lipschitz function on the p-adic field. We proved that the commutator is bounded from Lebesgue space to certain Campanato space.
基金supported by the National Natural Science Foundation of China(Nos.12471394,12371417)Natural Science Foundation of Changsha(No.kq2502101)。
文摘This paper aims to investigate the tamed Euler method for the random periodic solution of semilinear SDEs with one-sided Lipschitz coefficient.We introduce a novel approach to analyze mean-square error bounds of the novel schemes,without relying on a priori high-order moment bound of the numerical approximation.The expected order-one mean square convergence is attained for the proposed scheme.Moreover,a numerical example is presented to verify our theoretical analysis.
