The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to mod...The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.展开更多
Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the co...Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.展开更多
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e...The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.展开更多
Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid...Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.展开更多
For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined b...For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.展开更多
Discusses the use of the notion of fuzzy point to study some basic algebraic structures, such as group, semi group and ideal and then clarifies the links between the fuzzy point approach and the classical fuzzy approach.
Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The nece...Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.展开更多
This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Un...This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution.展开更多
基金supported by the Natural Science Foundation of Yunnan Province (2011FB074)
文摘The purpose of this article is first to introduce the concept of multi-valued to- tally Quasi-φ-asymptotically nonexpansive semi-groups, which contains many kinds of semi- groups as its special cases, and then to modify the Halpern-Mann-type iteration algorithm for multi-valued totally Quasi-cS-asymptotically nonexpansive semi-groups to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in this article improve and extend the corresponding results announced by many authors recently.
基金Project supported by the Natural Science Foundation of Sichuan Province of China(No.2005A132)
文摘Some strong convergence theorems of explicit composite iteration scheme for nonexpansive semi-groups in the framework of Banach spaces are established. Results presented in the paper not only extend and improve the corresponding results of ShiojiTakahashi, Suzuki, Xu and Aleyner-Reich, but also give a partially affirmative answer to the open questions raised by Suzuki and Xu.
基金supported by the Natural Science Foundation of Yibin University (No. 2007Z3)
文摘The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
文摘Large deviations estimates for Poisson processes estimate the logarithm of rare events associated to a Poisson process which has more and more jump which are smaller and smaller. In stochastic analysis, they are valid on the whole path space. Asoociated to this jump process is a Markov semi-group. We translate in semi group theory the proof of Wentzel-Freidlin for these estimates by translating in semi-group theory some basical tools of stochastic analysis as the exponential martingales of stochastic analysis. These Wentzel-Freidlin estimates （upper-bound） are only true for the semi-group.
文摘For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.
文摘Discusses the use of the notion of fuzzy point to study some basic algebraic structures, such as group, semi group and ideal and then clarifies the links between the fuzzy point approach and the classical fuzzy approach.
基金This research is supported by the National Natural Science Foundation of China under Grant No.60674018.
文摘Exponential stability of the first order singular distributed parameter systems is discussedin the light of degenerate semi-group methods,which is described by the abstract developing equationin Hilbert space.The necessary and sufficient conditions concerning the exponential stability of thefirst order singular distributed parameter systems are given.
文摘This paper is concerned with a modified transitional Korteweg-de Vries equation ut+f(t)u2ux+uxxx=0, (x,t)∈R+×R+with initial value u(x,0)=g(x)∈H4(R+)and inhomogeneous boundary value u(0,t)=Q(t)∈C2([ 0,∞ )). Under the conditions either 1) f(t)≤0, f′(t)≥0or 2) f(t)≤−αwhere α>0, we prove the existence of a unique global classical solution.
