本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Ra...本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.展开更多
Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article give...Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability. As a consequence, the authors obtain its Hyers-Ulam stability and prove that the equation has a unique multivalued solution near an approximate multivalued solution.展开更多
In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in ?with init...In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in ?with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given.展开更多
Let X and Y be real Banach spaces. The stability of Hyers Ulam Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S→Y satisfying ‖ f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all ...Let X and Y be real Banach spaces. The stability of Hyers Ulam Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S→Y satisfying ‖ f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all x,y∈S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q ≥2 or Y is the L q(Ω,,μ) (1<q <+∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that (x,y)=‖x‖ p+‖y‖ p or (x,y)=‖x-y‖ p for p ≠1 is investigated.展开更多
In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta.
In this paper, using Banach’s contraction principle, we consider the Hyers-UlamRassias stability of nonlinear partial diferential equations. An example is given to demonstrate the applicability of our results.
文摘本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.
基金Supported by NSFC(10171014)Doctoral Programme Foundation of Institution of Higher Education and the Foundational of Fujian Educational Committee(JA02166)
文摘Because multifunctions do not have so good properties as single-valued functions, only the existence of solutions of the polynomial-like iterative equation of order 2 is discussed for multifunctions. This article gives conditions for its Hyers-Ulam-Rassias stability. As a consequence, the authors obtain its Hyers-Ulam stability and prove that the equation has a unique multivalued solution near an approximate multivalued solution.
文摘In this paper we apply the Fourier transform to prove the Hyers-Ulam-Rassias stability for one dimensional heat equation on an infinite rod. Further, the paper investigates the stability of heat equation in ?with initial condition, in the sense of Hyers-Ulam-Rassias. We have also used Laplace transform to establish the modified Hyers-Ulam-Rassias stability of initial-boundary value problem for heat equation on a finite rod. Some illustrative examples are given.
文摘Let X and Y be real Banach spaces. The stability of Hyers Ulam Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S→Y satisfying ‖ f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all x,y∈S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q ≥2 or Y is the L q(Ω,,μ) (1<q <+∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that (x,y)=‖x‖ p+‖y‖ p or (x,y)=‖x-y‖ p for p ≠1 is investigated.
文摘In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta.
文摘In this paper, using Banach’s contraction principle, we consider the Hyers-UlamRassias stability of nonlinear partial diferential equations. An example is given to demonstrate the applicability of our results.
