The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly ...The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.展开更多
The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is re...The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.展开更多
In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invari...In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invariant points. Moreover, we can see that M?bius transformation is hyperbolic isometries that form a group action PSL (2, R) on the upper half plane model.展开更多
This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.
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
Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonex...Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^（i）} [1, ∞） （i = 1, 2）, and F ：= F（T1）∩ F（T2） ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^＊ has Kadec-Klee property, then weak convergence theorems are obtained.展开更多
Consider the following auxiliary linear systems（1）（2）where A<sub>j</sub>,B<sub>j</sub> and C<sub>j</sub> satisfy certain recursion relations（see Refs.[1]and[2]for details）.The...Consider the following auxiliary linear systems（1）（2）where A<sub>j</sub>,B<sub>j</sub> and C<sub>j</sub> satisfy certain recursion relations（see Refs.[1]and[2]for details）.Thecompatibility condition of（1）and（2）gives rise to the KdV hierarchyqt<sub>2n+1</sub>=4DL<sup>n</sup>q,L=-（1/4）\展开更多
This paper investigates the fixed-point smoothing problems for linear discrete-time systems with multiple time-delays in the observations. The linear discrete-time systems considered have 1 ＋ 1 output channels. One i...This paper investigates the fixed-point smoothing problems for linear discrete-time systems with multiple time-delays in the observations. The linear discrete-time systems considered have 1 ＋ 1 output channels. One is instanta- neous observation and the others are delayed. The fixed-point smoothers involving recursive algorithm and non-recursive algorithm are designed by using innovation analysis theory without relying on the system augmentation approach. Also, it is further shown that the design of fixed-point smoother comes down to solving 1 ＋ 1 Riccati equations with the same dimensions as the original systems.展开更多
This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem a...This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.展开更多
The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite ...The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.展开更多
There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = ...There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.展开更多
文摘The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.
文摘The present paper is devoted to a novel smoothing function method for convex quadratic programming problem with mixed constrains, which has important application in mechanics and engineering science. The problem is reformulated as a system of non-smooth equations, and then a smoothing function for the system of non-smooth equations is proposed. The condition of convergences of this iteration algorithm is given. Theory analysis and primary numerical results illustrate that this method is feasible and effective.
文摘In this paper, I have provided a brief introduction on M?bius transformation and explored some basic properties of this kind of transformation. For instance, M?bius transformation is classified according to the invariant points. Moreover, we can see that M?bius transformation is hyperbolic isometries that form a group action PSL (2, R) on the upper half plane model.
基金Supported by the National 973-Project from MOST and Trans-Century Training Programme Foundation for the Talents by Ministry of Education and the Postdoctoral Foundation of China.
文摘This article considers the existence of solution for a boundary value problem of fractional order, involving Caputo＇s derivative{C0D^δtu（t）=g（t,u（t））,0〈t〈1,1〈δ〈2,u（0）α≠0,u（1）=β≠0.
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.
文摘Let E be a real uniformly convex and smooth Banach space, and K be a nonempty closed convex subset of E with P as a sunny nonexpansive retraction. Let T1, T2 ： K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with a sequence {kn^（i）} [1, ∞） （i = 1, 2）, and F ：= F（T1）∩ F（T2） ≠ 0. An iterative sequence for approximation common fixed points of the two nonself asymptotically nonexpansive mappings is discussed. If E has also a Frechet differentiable norm or its dual E^＊ has Kadec-Klee property, then weak convergence theorems are obtained.
基金Project supported by the National Basic Research Project"Nonlinear Science".
文摘Consider the following auxiliary linear systems（1）（2）where A<sub>j</sub>,B<sub>j</sub> and C<sub>j</sub> satisfy certain recursion relations（see Refs.[1]and[2]for details）.Thecompatibility condition of（1）and（2）gives rise to the KdV hierarchyqt<sub>2n+1</sub>=4DL<sup>n</sup>q,L=-（1/4）\
基金supported by the National Natural Science Foundation of China(Nos.61273124,61074038)the Nature Science Foundation of Shandong Province(No.Y2008G04)+3 种基金the China Postdoctoral Science Foundation(No.2011M501132)the Special Funds for Postdoctoral Innovative Projects of Shandong Province(No.201103043)the Doctoral Foundation of Taishan University(No.Y11-2-02)the Project of Shandong Province Higher Education Science and Technology Program(No.J12LN90)
文摘This paper investigates the fixed-point smoothing problems for linear discrete-time systems with multiple time-delays in the observations. The linear discrete-time systems considered have 1 ＋ 1 output channels. One is instanta- neous observation and the others are delayed. The fixed-point smoothers involving recursive algorithm and non-recursive algorithm are designed by using innovation analysis theory without relying on the system augmentation approach. Also, it is further shown that the design of fixed-point smoother comes down to solving 1 ＋ 1 Riccati equations with the same dimensions as the original systems.
文摘This paper is concerned with an Initial Boundary Value Problem (IBVP) for a strongly coupled semilinear reaction-diffusion system. By using the upper and lower solutions method and Leray-Schauder fixed point theorem and so on, the authors prove the global existence and uniqueness of a. smooth. solution for this IBVP under some appropriate conditions.
基金Supported by NSFC(Grant Nos.11171172 and 11401063)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20120002110044)the Natural Science Foundation of Chongqing(Grant No.cstc2014jcyj A00016)
文摘The purpose of this paper is to study a new viscosity iterative algorithm based on a generalized contraction for finding a common element of the set of solutions of a general variational inequality problem for finite inversely strongly accretive mappings and the set of common fixed points for a countable family of strict pseudo-contractions in uniformly smooth Banach spaces. We prove some strong convergence theorems under some suitable conditions. The results obtained in this paper improve and extend the recent ones announced by many others in the literature.
基金supported by the National Science Center,Poland(Grant No.UMO2014/15/B/ST1/01710)
文摘There are two algebraic lower bounds of the number of n-periodic points of a self-map f ： M →4 M of a compact smooth manifold of dimension at least 3： NFn（f） = min{#Fix（gn）;g - f; g continuous} and NJDn（f） = min{#Fix（gn）;g - f; g smooth}. In general, NJDn（f） may be much greater than NFn（f）. We show that for a self-map of a semi-simple Lie group, inducing the identity fundamental group homomorphism, the equality NFn（f） = NJDn（f） holds for all n →← all eigenvalues of a quotient cohomology homomorphism induced by f have moduli ≤ 1.
