A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma

This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question.

SET-VALUED CARISTI’S FIXED POINT THEOREM AND EEELAND’S VARIATIONAL PRINCIPLE

This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].

A Study of Caristi’s Fixed Point Theorem on Normed Space and Its Applications

In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem.

CARISTI TYPE HYBRID FIXED POINT THEOREMS IN MENGERPROBABILISTIC METRIC SPACE

This paper brings forward the concept of Caristi type hybrid fixed point in M-PM-space, by giving two hybrid fixed point theorems and two common hybrid fixed point theorems of sequences of set-valued mappings, the theorems improve and generalize the Caristi's fixed point and correspond to recent important results.

Caristi’s Fixed Point Theorem in G-Cone Metric Spaces and Application

In this work, we introduce a few versions of Caristi’s fixed point theorems in G-cone metric spaces which extend Caristi’s fixed point theorems in metric spaces. Analogues of such fixed point theorems are proved in this space. Our work extends a good number of results in this area of research.

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.

More on Fixed Point Theorem of {a, b, c}-Generalized Nonexpansive Mappings in Normed Spaces

Let X be a weakly Cauchy normed space in which the parallelogram law holds, C be a bounded closed convex subset of X with one contracting point and T be an {a,b,c}-generalized-nonexpansive mapping from C into C. We prove that the infimum of the set {‖x-T（x）‖} on C is zero, study some facts concerning the {a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton. Depending on the fact that the {a,b,0}-generalized-nonexpansive mapping from C into C has fixed points, accord- ingly, another version of the Browder＇s strong convergence theorem for mappings is given.

Common Fixed Point Theorems of Single-valued and Set-valued Mappings in Complete,Convex Metric Spaces

Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.

AN APPLICATION OF SCHAUDER’S FIXED POINT THEOREM TO THE EXISTENCE OF SOLUTlONS OF IMPULSIVELY DIFFERENTIAL EQUATIONS

In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed point theorem,whichimproves some existing results.

Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay

For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.

The Generalization of Ciric and Caristi Type Fixed Point Theorem

In this paper,we generalize the renowned Ciric and Caristi type fixed point theorem and some corollaries.Then we give an example to illustrate our result is really better than the theorem.

具有饱和恢复率的SEIR时滞模型的行波解

研究一类具有饱和恢复率的SEIR时滞模型的行波解.首先,考虑一类二维系统初值问题的适定性;然后,通过构造一对有界的向量值上、下解得到一个闭凸集;最后,利用Schauder不动点定理证明:当基本再生数R^(0)>1,波速c>c^(*)时模型存在非平凡行波解.

Menger概率度量空间中Caristi型混合不动点定理

本文在Menger概率度量空间中引进Caristi型混合不动点概念，得到两个混合不动点定理和两个集值映象序列的公共混合不动点定理，我们的定理改进和推广了Caristi不动点定理及相关的近期重要结果．

扩张型随机算子的随机不动点定理和Caristi不动点定理的随机类比

关于压缩型和非扩张型随机算子的随机不动点定理,已有很多结果,但关于扩张型随机算子的随机不动点定理,目前文献中尚未见到。本文对具有随机定义域的扩张型随机算子证明了两个随机不动点定理。本文还对一族依赖于参数的偏序集证明了可测的极大元映射的存在性引理,并用之证明了重要的Caristi不动点定理的随机类比。

Caristi不动点定理中集值映射的稳定性

证明了从Caristi不动点定理中下半连续,下有界的泛函组成的空间到满足Caristi不动点定理条件的映射组成的空间的集值映射是几乎下半连续的.另外还证明了Caristi不动点定理中对应映射组成的空间是完备的.

Caristi不动点定理与Banach压缩原理的等价性

作者证明了在一定条件下存在某一等价度量d*,使得满足Caristi不动点定理条件的映射F关于d*是Banach压缩映射,因此,Caristi不动点定理在一定条件下与Banach压缩映射原理等价.

Ekeland变分原理与Caristi不动点定理的另一种相关性

在Ekeland变分原理和Caristi不动点定理等价的基础上,进一步证明了Ekeland变分原理中的ε-极值点包含在Caristi不动点定理中对应映射的不动点集中.

非对称度量空间中广义Caristi不动点定理

将非对称度量空间中Caristi不动点定理从单值映射拓广到集值映射情形,进一步地,得到了几个广义Caristi不动点定理.

有序集中Caristi定理的一个推广

通过对有序集的进一步研究,给出了有序集上的一个不动点定理,从而推广了有序集中Caristi定理的结果。

VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS

By using the properties of w-distances and Gerstewitz＇s functions, we first give a vectorial Takahashi＇s nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland＇s variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland＇s variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346（2008）, 9-16] are weakened or even completely relieved.