带非局部低阶项非线性抛物型方程的时间最优控制

考虑一个带非局部低阶项非线性抛物型方程的时间最优控制问题．首先利用Schauder不动点定理证明了系统的适定性，然后利用Carleman不等式和Kakutani不动点定理证明了容许控制和最优控制的存在性，并且建立了时间最优控制的最大值原理．     

Generalized KKM theorems and common fixed point theorems

In this paper, we first prove a generalized KKM theorem, and then use this generalized KKM theorem to establish the generalized equi-KKM theorem, common fixed point theorems for a family of multivalued maps, and the Kakutani-Fan-Glicksberg fixed point theorem. We also show that an existence theorem of the common fixed point theorem is equivalent to the Kakutani-Fan-Glicksberg fixed point theorem.     

Positive Solution of a Quadratic Integral Equation Using Generalization of Darbo’s Fixed Point Theorem

The objective of this article is to establish a fixed point theorem using different class of control functions, which is a generalization of Darbo’s fixed point theorem (DFPT) and its various versions obtained by several authors. Using this result we obtain existence of at least one positive solution for a quadratic integral equation of Fredholm type.     

Leray-Schauder不动点定理的一个新证明

给出Leray-Schauder不动点定理的一个新证明.我们首先给出集值映射的焊接引理,利用集值映射的焊接引理和Kakutani不动点定理证明Leray-Schauder不动点定理,并证明Leray-Schauder不动点定理与Brouwer不动点定理等价.     

概率度量空间中若干新的不动点定理*

本文提出了Z-M-PN空间的概念,在概率度量空间中我们得到了若干新的不动点定理。同时,一些着名的不动点定理在概率度量空间中得到了推广,诸如:Schauder不动点定理、郭大钧不动点定理和Petryshyn不动点定理被推广到M-PN空间;Altman不动点定理被推广到Z-M-PN空间。     

Feedback control systems governed by evolution equations

ABSTRACT

The goal of this paper is to provide systematic approaches to study the feedback control systems governed by evolution equations in separable reflexive Banach spaces. We firstly give some existence results of mild solutions for the equations by applying the Banach's fixed point theorem and the Leray–Schauder alternative fixed point theorem with Lipschitz conditions and some types of boundedness conditions. Next, by using the Filippove theorem and the Cesari property, a new set of sufficient assumptions are formulated to guarantee the existence of feasible pairs for the feedback control systems. Some existence results for an optimal control problem are given. Finally, we apply our main result to obtain a controllability result for semilinear evolution equations and existence results for a class of differential variational inequalities and Clarke's subdifferential inclusions.     

The existence of fixed points of left-continuous monotone operators in spaces with a regular cone

In theorems on the existence of a fixed point of an operator the latter is usually assumed to be continuous. In this paper we prove a theorem with sufficient conditions for the existence of a fixed point of an operator which is not necessarily continuous (possibly it is left-continuous). The obtained theorem with the use of regular cones is applied for proving the existence of a fixed point of a nonlinear integral operator. We give an example illustrating the theorem.     

向量值映射锥鞍点存在定理

本文首次通过借助Kakutani-Fan-Glicksberg固定点定理和非线性标量化,研究了向量值映射的Benson锥鞍点定理.然后,通过使用该Kakutani-Fan-Glicksberg固定点定理,同样得到了集值映射的锥松鞍点定理.     

L-空间中的KKM映射及不动点定理

引入了L-空间和L-空间上的KKM类映射，建立了关于该类映射的一些不动点定理，其中包括Schauder型和Fan-Browder型不动点定理．得到了L-空间中的KyFan匹配定理和叠合点定理．     

Generalizations of fixed point theorems and computation

As a powerful mechanism, fixed point theorems have many applications in mathematical and economic analysis. In this paper, the well-known Brouwer fixed point theorem and Kakutani fixed point theorem are generalized to a class of nonconvex sets and a globally convergent homotopy method is developed for computing fixed points on this class of nonconvex sets.     

A fixed point theorem including the last theorem of Poincaré

Poincaré's last theorem is the most famous among those theorems which are not subsumed by the Lefschetz fixed point theorem. A fixed point theorem is proved directly and constructively which in a special case reduces to the last theorem of Poincaré.     

凸幂凝聚算子的不动点定理及其对抽象半线性发展方程的应用

从应用问题的需要出发,给出了一类新的算子-凸幂凝聚算子的定义,推广了凝聚算子的概念,并证明了这类新算子的不动点定理,从而推广了著名的Schauder不动点定理和Sadovskii不动点定理.作为应用,获得了Banach空间中一类具有非紧半群的半线性发展方程初值问题整体mild解和正mild解的存在性.     

Remarks on Caristi’s fixed point theorem and Kirk’s problem

Without assumptions on the continuity and the subadditivity of η, by means of Caristi’s fixed point theorem, we investigated the existence of fixed points for a Caristi type mapping which partially answered Kirk’s problem and improved Caristi’s fixed point theorem, Jachymski’s fixed point theorem and Khamsi’s fixed point theorem since φ is not necessarily assumed to be bounded below on X.     

New Characterization of Geodesic Convexity on Hadamard Manifolds with Applications

In this paper, some new results, concerned with the geodesic convex hull and geodesic convex combination, are given on Hadamard manifolds. An S-KKM theorem on a Hadamard manifold is also given in order to generalize the KKM theorem. As applications, a Fan–Browder-type fixed point theorem and a fixed point theorem for the a new mapping class are proved on Hadamard manifolds.     

Mild Solution and Fractional Optimal Control of Semilinear System with Fixed Delay

This paper considers fractional optimal control of a semilinear system with fixed delay in a reflexive Banach space. The existence and uniqueness of mild solution are obtained using the Weissinger’s fixed point theorem. The existence of optimal control for the system governed by fractional-order semilinear equation with fixed delay in state is presented. To show the effectiveness of the developed theory, an example is given.     

A new type of fixed point theorem in metric spaces

We prove a generalization of Edelstein’s fixed point theorem. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem.     

非紧超凸度量空间中的一个新的不动点定理及其对鞍点问题的应用

In this paper,a new fixed point theorem is established in noncompact hyperconvex metric spaces.As applications,a continuous selection and its fixed point theorem,an existence theorem for maximal elements,a Ky Fan minimax inequality and an existence theorem for saddle points are obtained.     

非紧超凸度量空间中的一个新的不动点定理及其对鞍点问题的应用

在非紧超凸度量空间中建立了一个新的不动点定理.作为应用,研究了连续选择及其不动点定理,极大元定理、Ky Fan极大极小不等式和鞍点定理.     

Existence of solutions for nonlinear high-order fractional boundary value problem with integral boundary condition

The main purpose of this paper is to present the existence results of solutions and positive solutions of nonlinear high-order fractional boundary value problems with integral boundary condition. By using the Banach fixed point theorem and the Krasnosel’skii fixed point theorem, we obtain the existence and uniqueness of real solution. By the Guo–Krasnosel’skii fixed point theorem on the cone, we obtain a desired result for guaranteeing the existence of positive solution. Several interesting examples relevant to the main results are also considered.     

From an abstract maximal element principle to optimization problems,stationary point theorems and common fixed point theorems

In this paper, we first establish an existence theorem related with intersection theorem, maximal element theorem and common fixed point theorem for multivalued maps by applying an abstract maximal element principle proved by Lin and Du. Some new stationary point theorems, minimization problems, new fixed point theorems and a system of nonconvex equilibrium theorem are also given.