FIXED POINT RESULTS ON METRIC-TYPE SPACES

In this paper we obtain fixed point and common fixed point theorems for self- mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.     

GENERALIZED WARDOWSKI TYPE FIXED POINT THEOREMS VIA α-ADMISSIBLE FG-CONTRACTIONS IN b-METRIC SPACES

Recently, Wardowski [Fixed Point Theory Appl., 2012: 94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. In this paper, we introduce an α-β-FG-contraction and generalize the Wardowski fixed point result in b-metric and ordered b-metric spaces. As an application of our results we deduce Suzuki type fixed point results for β-FG-contractions.Moreover, we discuss some illustrative examples to highlight the realized improvements.     

A Continuation Method for Solving Fixed Point Problems in Unbounded Convex Sets

In this paper, an unbounded condition is presented, under which we are able to utilize the interior point homotopy method to solve the Brouwer fixed point problem on unbounded sets. Two numerical examples in R3 are presented to illustrate the results in this paper.     

DYNAMICAL CONSISTENCE IN 3-DIMENSIONAL TYPE-K COMPETITIVE LOTKA-VOLTERRA SYSTEM

A 3-dimensional type-K competitive Lotka-Volterra system is considered in this paper. Two discretization schemes are applied to the system with an positive interior fixed point, and two corresponding discrete systems are obtained. By analyzing the local dynamics of the corresponding discrete system near the interior fixed point, it is showed that this system is not dynamically consistent with the continuous counterpart system.     

Almost Fixed Points and Fixed Points of Upper [Lower] Semicontinuous Multimap on Locally G-convex Spaces

In this paper, we use the well known KKM type theorem for generalized convex spaces due to Park (Elements of the KKM theory for generalized convex spaces, Korean J. Comp. Appl. Math., 7(2000), 1-28) to obtain an almost fixed point theorem for upper [resp., lower] semicontinuous multimaps in locally G-convex spaces, and then give a fixed point theorem for upper semicontinuous multimap with closed Г-convex values.     

EXISTENCE RESULTS FOR IMPULSIVE NEUTRAL EVOLUTION DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

This paper is mainly concerned with the existence of mild solutions to a first order impulsive neutral evolution differential equations with state-dependent delay. By suitable fixed point theorems combined with theories of evolution systems,we prove some existence theorems. As an application,an example is also given to illustrate the obtained results.     

ALMOST PERIODICITY FOR AN IMPULSIVE PURE DELAY LOGISTIC EQUATION

By employing a fixed point theorem in cones,we investigate the existence of almost periodic solutions to an impulsive pure delay Logistic equation. A set of suffcient conditions for the existence of almost periodic solutions to the equation are obtained.     

HORN-TYPE THEOREM IN FRéCHET SPACES AND APPLICATION~(**)

This paper establishes a Horn-type fixed point theorem in Fréchet spaces which is ananswer to Burton's problem in these spaces.As an application of the result,the authorsobtain an existence theorem of periodic solutions for functional differential equations withinfinite delay.     

POSITIVE SOLUTIONS TO PERIODIC BOUNDARY VALUE PROBLEM OF SINGULAR SEMI-POSITONE NONLINEAR THIRD-ORDER ORDINARY DIFFERENTIAL EQUATIONS

By means of nonlinear alternative of Leray-Schauder type and Schauder fixed point theorem, the existence of positive solutions to singular semi-positone nonlinear third-order differential equations are established. The results are illustrated with an example.     

Banach空间非线性二阶脉冲奇异积分-微分方程积分边值问题的正解

The existence of positive solutions to a boundary value problem of second-order impulsive singular integro-differential equation with integral boundary conditions in a Banach space is obtained by means of fixed point theory.Moreover,an application is also given to illustrate the main result.     

不动点定理

我们将求算子T的不动点的问题,转化为寻找一个算子F,若乘积TF可换且有唯一不动点,则T必有不动点。 对所有具有唯一性的不动点定理,均可利用本文定理1而得到推广。文中定理2至定理8即属此情形(也有一些对定理本身作了改进)。 定理1 设T,F均为映距离空间X到自身的算子。若方程组     

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.     

Order Extensions and the Fixed Point Property

The purpose of this paper is to investigate how the fixed point property and its negation behave when a covering relation is added to the order. We prove that every finite ordered set which is not totally ordered and which is dismantlable by retractables, respectively by irreducibles, has an upper cover (in its extension lattice) which is also dismantlable by retractables, respectively by irreducibles. We also provide examples of finite ordered sets having the fixed point property so that none of their upper covers has the fixed point property. Part of this work was done while the author was visiting Brandon University. The author thanks M. Roddy for his hospitality and financial support.     

Strong Convergence of a Split Common Fixed Point Problem

In this article, we present a new general algorithm for solving the split common fixed point problem in an infinite dimensional Hilbert space, which is to find a point which belongs to the common fixed point of a family of quasi-nonexpansive mappings such that its image under a linear transformation belongs to the common fixed point of another family of quasi-nonexpansive mappings in the image space. We establish the strong convergence for the algorithm to find a unique solution of the variational inequality, which is the optimality condition for the minimization problem. The algorithm and its convergence results improve and develop previous results in this field.     

On Fixed Point and Almost Fixed Point Problems of Lower Semicontinuous Type Multivalued Mappings

In the present paper, some new almost fixed point theorems and fixed point theorems for lower semicontinuous type multivalued mappings are obtained in metrizable H-spaces.     

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.     

Caristi 不动点定理的推广及应用

本文推广了古典的Garisti不动点定理,作为应用,古典的Ekeland变分原理得到了推广,并且证明了推广的Garisti不动点定理和推广的Ekeland变分原理是等价的．     

局部$G$-凸一致空间上几乎不动点定理和不动点定理

得到局部G-凸一致空间上具有S-KKM性质的集值映射的新的几乎不动点定理和不动点定理.我们的结果对已有文献中的相应结论进行了改进和一般化.     

A Fixed Point Theorem and an Equilibrium Point of an Abstract Economy in <Emphasis Type="Italic">H</Emphasis>-spaces

In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4].