没有开纤维的广义拟均衡问题(英文)

In this paper, we first prove some new selection and fixed point theorems in generalized convex spaces. Then, we establish some existence theorems of quasi-equilibrium and generalized quasi-equilibrium without the conditions of open fibers, by applying our selection and fixed point theorems.     

A general stochastic fixed-point theorem for continuous random operators on stochastic domains

We prove that under certain conditions a continuous random operator with stochastic domain has a random fixed point provided that each realization has a (deterministic) fixed point. As a by-product we obtain a selection theorem for the interior of certain convex-valued measurable correspondences. We apply our results to obtain stochastic Krasnoselski- and Rothe-type theorems and existence results for random differential and integral equations.     

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.     

Stationary points and equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game-theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path following methods to find a stationary point and illustrate such methods by an example. Finally, we discuss some refinements of stationary points and their application to solve the problem of equilibrium selection.     

Fixed Point and Equilibrium Theorems in a Generalized Convexity Framework

We study the fixed point property of set-valued maps and the existence of equilibria in the framework of $\mathbb{B}$ -convexity, recently defined by W. Briec and Ch. Horvath. We introduce some classes of the set-valued maps with generalized convexity and prove continuous selection and fixed point properties for them. Finally, we obtain results concerning the existence of quasi-equilibria for W.K. Kim’s new model.     

On the existence of positive solution for second-order multi-points boundary value problems

Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically.     

含积分边界条件的分数阶微分方程边值问题的正解的存在性

研究了含积分边界条件的分数阶微分方程的边值问题,首先给出格林函数及性质,其次将问题转化为一个等价的积分方程,最后应用Krasnoselkii及Leggett-Williams不动点定理得到了一个及多个正解的存在性,推广了以往的结果．     

Generalizations of Darbo’s fixed point theorem and solvability of integral and differential systems

In this paper, we establish some new generalizations of Darbo’s fixed point theorem for multivalued mappings. Moreover, we prove the existence of solutions for a class of integral equations by Darbo’s fixed point theorem and the existence of solutions for a class of differential inclusions using a generalization of Darbo’s fixed point theorem.     

超凸空间上一类非扩张集值映象的性质

研究超凸空间上具有非空闭球交值的非扩张集值映象的不动点及近似不动点的存在性，以及其单值非扩张选择的唯一性问题.     

Collective fixed points, generalized games and systems of generalized quasi-variational inclusion problems in topological spaces

In this paper, by using a fixed point theorem for expansive set-valued mappings with noncompact and nonconvex domains and ranges in topological spaces due to the author, we first prove a collective fixed point theorem and an existence theorem of equilibrium points for a generalized game. As applications, some new existence theorems of solutions for systems of generalized quasi-variational inclusion problems are established in noncompact topological spaces. Our results are different from known results in the literature.     

Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations

In this article, we study a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations. We obtain sufficient conditions for existence and uniqueness of positive solutions. We use the classical fixed point theorems such as Banach fixed point theorem and Krasnoselskii’s fixed point theorem for uniqueness and existence results. As in application, we provide an example to illustrate our main results.     

Generalized vector quasi-equilibrium problems with applications

In this paper, we consider the generalized vector quasi-equilibrium problem with or without involving Φ-condensing maps and prove the existence of its solution by using known fixed point and maximal element theorems. As applications of our results, we derive some existence results for a solution to the vector quasi-optimization problem for nondifferentiable functions and vector quasi-saddle point problem.     

一类反向混合单调算子新不动点定理的推广

利用锥理论和非对称迭代方法,讨论了一类反向混合单调算子的不动点的存在唯一性,得到了若干不具有连续性和紧性条件的有关反向混合单调算子的新不动点定理,所得结果是某些已有结果的本质改进和推广.     

Existence of positive solutions for fourth-order m-point boundary value problem with variable parameters

In this paper, we investigate the existence of positive solutions for a class of nonlinear fourth-order m-point boundary value problem with two variable parameters. By using the fixed point index theory, we give some new existence results.     

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 best proximity pairs and equilibrium pairs

In this paper, using the fixed point theorem for Kakutani factorizable multifunctions, we shall prove new existence theorems of best proximity pairs and equilibrium pairs for free abstract economies, which include the previous fixed point theorems and equilibrium existence theorems.     

Stampacchia generalized vector quasi-equilibrium problem with set-valued mapping

In this paper, the solvability of Stampacchia generalized vector quasi-equilibrium problem (in short, GVQEP) with set-valued mapping is studied. By using continuous selection theorem and fixed point theorems, some existence theorems for (GVQEP) are obtained without any monotonicity assumption. These theorems unify and improve some results in the recent references.     

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.     

Positive solutions for a Floquet functional boundary value problem

In this paper we prove the existence of multiple positive solutions for a boundary value problem concerning a first order functional differential equation. The results are obtained by using two fixed point theorems on appropriate cones in Banach spaces. These theorems are based on the fixed point index theory.