函数方程的实解

In this paper the asymptotieal stability in p-moment of neutral stochastic differential equations with discrete and distributed time-varying delays is discussed. The authors apply the fixed-point theory rather than the Lyapunov functions. We give a sufficient condition for asymptotical stability in p-moment when the coefficient functions of equations are not required to be fixed values. Since more general form of system is considered, this paper improves Luo Jiaowan＇s results.     

脉冲比较微分系统解的φ0-稳定性

本文主要利用分段连续的Lyapunov函数得到脉冲比较微分系统(2)的φ0-稳定性,并且通过比较方程,得到脉冲微分系统(1)的稳定性.     

STABILITY OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper,we obtain suffcient conditions for the stability in p-th moment of the analytical solutions and the mean square stability of a stochastic differential equation with unbounded delay proposed in [6,10] using the explicit Euler method.     

COMMON FIXED POINTS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

For a subset K of a metric space (X , d) and x ∈ X ,P K (x) ={y ∈ K : d(x, y) = d(x, K) ≡ inf { d(x, k) : k ∈ K }}is called the set of best K-approximant to x. An element g。∈ K is said to be a best simultaneous approximation of the pair y 1 , y 2 ∈ X if max{d(y 1 , g。), d(y 2 , g。) } = inf g ∈ K max { d(y 1 , g), d(y 2 , g)}.In this paper, some results on the existence of common fixed points for Banach operator pairs in the framework of convex metric spaces have been proved. For self mappings T and S on K, results are proved on both T - and S- invariant points for a set of best simultaneous approximation. Some results on best K-approximant are also deduced. The results proved generalize and extend some results of I. Beg and M. Abbas [1] , S. Chandok and T.D. Narang [2] , T.D. Narang and S. Chandok [11] , S.A. Sahab, M.S. Khan and S. Sessa [14] , P. Vijayaraju [20] and P. Vijayaraju and M. Marudai [21] .     

A REMARK ON CERTAIN DIFFERENTIAL INEQUALITIES INVOLVING p-VALENT FUNCTIONS

In the present paper,we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity.We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.     

渐近φ伪压缩映象有限族的迭代程序的强收敛(英文)

Strong convergence theorems for approximation of common fixed points of asymptoticallyφ-quasi-pseudocontractive mappings and asymptoticallyφ-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new compos- ite implicit iteration scheme with errors.The results presented in this paper extend and improve the main results of Sun,Gu and Osilike published on J.Math.Anal. Appl.     

GENERALIZED DHALQUIST CONSTANT WITH APPLICATION IN STABLE ANALYSIS FOR DYNAMIC SYSTEMS ON TIME SCALES

A novel and effective approach to exponentially stable analysis for dynamic systems on time scales is investigated using the nonlinear operator named the generalized Dahlquist constant in this paper, and simple yet generic criteria are derived ensuring the robust stability.     

The Stable Farkas Lemma for composite convex functions in infinite dimensional spaces

In this paper, we consider a general composite convex optimization problem with a cone-convex system in locally convex Hausdorff topological vector spaces. Some Fenchel conjugate transforms for the composite convex functions are derived to obtain the equivalent condition of the Stable Farkas Lemma, which is formulated by using the epigraph of the conjugates for the convex functions involved and turns out to be weaker than the classic Slater condition. Moreover, we get some necessary and sufficient conditions for stable duality results of the composite convex functions and present an example to illustrate that the monotonic increasing property of the outer convex function in the objective function is essential. Our main results in this paper develop some recently results.     

Shrinking Projection Methods for a Family of Quasi-φ-Strict Asymptotically Pseudo-Contractions in Banach Spaces

The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property (K). The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.     

Banach空间中一族拟$\phi$-严格渐近伪压缩映像的收缩投影方法

The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property （K）. The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.     

Positive energy theorem for (4+1)-dimensional asymptotically anti-de Sitter spacetimes

We define the total energy-momenta for(4+1)-dimensional asymptotically anti-de Sitter spacetimes,which comes from the boundary terms at infinity in the integral form of the Weitzenbck formula.Then we prove the positive energy theorem for such spacetimes,following Witten’s original argumentsfor the positive energy theorem in asymptotically flat spacetimes.     

关于运用Liapunov函数的滞后型系统部分稳定性的注释

Sufficient conditions for the stability with respect to part of the functional differential equation variables are given. These conditions utilize Lyapunov functions to determine the uniform stability and uniform asymptotic stability of functional differential equations. These conditions for the partial stability develop the Razumikhin theorems on uniform stability and uniform asymptotic stability of functional differential equations. An example is presented which demonstrates these results and gives insight into the new stability conditions.     

Absolute stability of general lurie type indirect control systems

1. IntroductionThe absolute stability problem is one of the central topics of the stability theory for itstheoretical and engineering importance. UP to date, this problem has been studied by manyauthors [1--9], and many sufficient conditions and some necessary and sufficiellt conditions inspecial cases for absolute stability are obtained. In papers [7,8], Liao gave a necessary andsufficient condition for absolute stability for partial arguments. In this paperg by using anew concept of absolut…     

EQUICONTINUITY OF TRIANGULAR MAPS

In this paper we study the equicontinuity of a triangular map of the square,and obtain some equivalent conditions for it.     

Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations

We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When θ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.     

NONLINEAR STABILITY OF NATURAL RUNGE-KUTTA METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonlinear NDDEs, are given. In particular, it is shown that the (k, l)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.     

STABILITY OF THEORETICAL SOLUTION AND NUMERICAL SOLUTION OF NONLINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE DELAYS

This paper is concerned with the stability of theoretical solution and numerical solutionof a class of nonlinear differential equations with piecewise delays.At first,a sufficientcondition for the stability of theoretical solution of these problems is given,then numericalstability and asymptotical stability are discussed for a class of multistep methods whenapplied to these problems.     

Topological Tail Pressure for Asymptotically Sub-additive Continuous Potentials

We define the topological tail pressure and the conditional pressure for asymptotically sub-additive continuous potentials on topological dynamical systems and obtain a variational principle for the topological tail pressure without any additional assumptions.     

STABILITY ANALYSIS OF FUZZY DIFFERENTIAL EQUATIONS WITH DELAY

In this paper,the exponential stability of fuzzy differential equations with delay is investigated.By employing the formula for the variation of parameters, inequality technique and the norm and measure of matrix,an algebraic criterion for the exponential stability is obtained.