In this paper, by applying the fixed point alternative method, we give a necessary and sufficient condition in order that the first order linear system of differential equationsż(t) + A(t)z(t) + B(t) = 0 has the Hyers-Ulam-Rassias... more
In this paper, by applying the fixed point alternative method, we give a necessary and sufficient condition in order that the first order linear system of differential equationsż(t) + A(t)z(t) + B(t) = 0 has the Hyers-Ulam-Rassias stability and find Hyers-Ulam stability constant under those conditions. In addition to that we apply this result to a second order differential equationÿ(t) + f (t)ẏ(t) + g(t)y(t) + h(t) = 0.
In this paper we established the Hyers-Ulam-Rassias stability of a linear differential equation of second order with initial condition. We also proved the Hyers-Ulam-Rassias stability of a nonlinear differential equation of second order... more
In this paper we established the Hyers-Ulam-Rassias stability of a linear differential equation of second order with initial condition. We also proved the Hyers-Ulam-Rassias stability of a nonlinear differential equation of second order with initial condition.
In this paper, we examine the relation between practical stability and Hyers-Ulam-stability and Hyers-Ulam-Rassias stability as well. In addition,by practical stability we gave a sufficient condition in order that the first order... more
In this paper, we examine the relation between practical stability and Hyers-Ulam-stability and Hyers-Ulam-Rassias stability as well. In addition,by practical stability we gave a sufficient condition in order that the first order nonlinear systems of differential equations has local generalized Hyers-Ulam stability and local generalized Hyers-Ulam-Rassias stability.
By using of the Gronwall inequality, we prove the Hyers-Ulam stability of differential equations of second order with initial conditions. ∞ 0 | ( )| = 0 and = inf ≥0 ( ) = .
In this article, we establish the superstability of diff erential equations of second order with boundary conditions or with initial conditions as well as the superstability of di fferential equations of higher order with initial... more
In this article, we establish the superstability of diff erential equations of second order with boundary conditions or with initial conditions as well as the superstability of di fferential equations of higher order with initial conditions.
Artificial Neural Networks (ANN's) are largely used in applications involving classification or functions approximation. It has been proved that several classes of ANN such as Multilayer Radial-Basis Function Networks (RBFN) are... more
Artificial Neural Networks (ANN's) are largely used in applications involving classification or functions approximation. It has been proved that several classes of ANN such as Multilayer Radial-Basis Function Networks (RBFN) are universal function approximators . Therefore, they are widely used for function approximation . In this paper ,we examine the similarities and differences between RBFNNs compare the performance of learning with each representation applied to the interpolation problem. Nonetheless, this paper should help the reader to understand which basis function and which efficient method should be employed for particular reconstruction problem. It should also encourage the reader to consult the literature pointed out in the bibliography for further studying.
In this paper ,we examine the similarities and differences between RBFNNs and compare the performance of learning, then we applied to the interpolation problem by using data of blood pressure disease which taken from health office in... more
In this paper ,we examine the similarities and differences between RBFNNs and compare the performance of learning, then we applied to the interpolation problem by using data of blood pressure disease which taken from health office in diwaniya city .
In this paper, we show the degree of approximation by a single hidden layer feed forward model with n units in the hidden layer is bounded below by the degree of approximation by a linear combination of n ridge functions. We prove that... more
In this paper, we show the degree of approximation by a single hidden layer feed forward model with n units in the hidden layer is bounded below by the degree of approximation by a linear combination of n ridge functions. We prove that there exists an analytic, strictly monotone, sigmoidal activation function for which this lower bound is essentially attained. Also we extend the Kolmogorov’s existence theorem to be apply at any compact set, (i.e., closed and bounded set) also we prove that a FFNN with one hidden layer can uniformly approximate any continuous function of several variable, f(x1, x2, …, xn), which is defined in compact set to any required accuracy.
We establish the generalized superstability of differential equations of nth-order with initial conditions and investigate the generalized superstability of differential equations of second order in the form of y′′(x) + p(x)y′(x)+q(x)y(x)... more
We establish the generalized superstability of differential equations of nth-order with initial conditions and investigate the generalized superstability of differential equations of second order in the form of y′′(x) + p(x)y′(x)+q(x)y(x) = 0 and the superstability of linear differential equations with constant coefficients with initial conditions.
In this article, we establish the superstability of differential equations of second order with boundary conditions or with initial conditions as well as the superstability of differential equations of higher order with initial conditions.
