Mizoguchi–Takahashi’s type common fixed point theorem

Recently Kamran extended the result of Mizoguchi and Takahashi for closed multi-valued mappings and proved a fixed point theorem. In this paper we further extend the result concluded by Kamran and prove a common fixed point theorem by using the concept of lower semi-continuity.     

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].     

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.     

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.     

Fixed Points of Sequence of Ćirić Generalized Contractions of Perov Type

Perov used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article, we study fixed point results for the new extensions of sequence of ?iri? generalized contractions on cone metric space, and we give some generalized versions of the fixed point theorem of Perov. The theory is illustrated with some examples. It is worth mentioning that the main result in this paper could not be derived from ?iri?’s result by the scalarization method, and hence indeed improves many recent results in cone metric spaces.     

A fixed point theorem for a family of mappings in a fuzzy metric space

In this paper we give a common fixed point theorem for a family of mappings of a G-complete fuzzy metric space (X, M, *) into itself. From this result we deduce a common fixed point theorem for a family of mappings of a complete metric space (X, d) into itself. Supported by University of Palermo.     

Existence of solutions and bifurcation points to Hammerstein equations with essentially bounded kernel

In this paper we establish an existence of solution theorem and an existence of bifurcation point theorem for Hammerstein integral equation whose kernel is supposed neither symmetric nor positive defined. To prove our result, we use the Tychonoff fixed point theorem. In particular, our bifurcation result is directly comparable with an analogous one recently established by F. Faraci.     

Positive solutions for a fractional boundary value problem with p-Laplacian operator

In this paper, we are mainly concerned with positive solutions for a p-Laplacian fractional boundary value problem. By virtue of Jensen’s inequalities and some new properties of the Green function of the problem, we adopt the Krasnoselskii-Zabreiko fixed point theorem to establish the results of existence and multiplicity of the positive solutions. Finally, a uniqueness theorem is established by using a fixed point theorem of concave operator and an example is given to illustrate the result.     

Higher order boundary value problems on time scales

In this paper we study the existence of solutions for Lidstone boundary value problems on time scale. Firstly, by using Schauder fixed point theorem in a cone, we obtain the existence of solutions to a Lidstone boundary value problem (LBVP). Secondly, existence result for this problem is also given by the monotone method. Finally, by using Krasnosel'skii fixed point theorem, it is proved that the LBVP has a positive solution.     

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.     

Fixed point results on a metric space endowed with a finite number of graphs and applications

In this paper, we consider self-mappings defined on a metric space endowed with a finite number of graphs. Under certain conditions imposed on the graphs, we establish a new fixed point theorem for such mappings. The obtained result extends, generalizes and improves many existing contributions in the literature including standard fixed point theorems, fixed point theorems on a metric space endowed with a partial order and fixed point theorems for cyclic mappings.     

Existence theorems for monotone operators in reflexive Banach spaces

In this paper, we obtain an existence theorem for single-valued monotone operators in a reflexive Banach space. Using this result, we prove a fixed point theorem for nonexpansive mappings in a Hilbert space and an existence theorem for maximal monotone operators in a Banach space. Received: 3 July 2006 Revised: 15 January 2007     

Nonlinear random elliptic boundary value problem

In this paper we obtain a solvability result for random elliptic boundary value problem. Our result extends Browder's [2] main theorem to the random case. We use author's [4] fixed point theorem for this purpose.     

Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces

In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces. Received: 10 August 2007     

Best proximity points: global minimization of multivalued non-self mappings

In this article, we give a best proximity point theorem for generalized contractions in metric spaces with appropriate geometric property. We also, give an example which ensures that our result cannot be obtained from a similar result due to Amini-Harandi (Best proximity points for proximal generalized contractions in metric spaces. Optim Lett, 2012). Moreover, we prove a best proximity point theorem for multivalued non-self mappings which generalizes the Mizoguchi and Takahashi’s fixed point theorem for multivalued mappings.     

一类新的KKM定理及其应用*

本文得到一类新的KKM定理,统一和改进了[2,3,0,7,11]中的结果。作为应用,我们得到了几个匹配定理、重合定理、不动点定理、极大极小不等式定理及截口定理。     

An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1].     

FC-空间中的不动点定理定理及应用

在FC-空间中建立了一个不动点定理,推广了近期文献的一个相关结论利用这个结果,我们建立了一些广义型定理,推广了著名的截口定理到FC-空间中借助这个截口定理,在FC-空间得到一些新的广义向量均衡问题解的存在性定理.     

A class of function spaces and its application in solving second-order nonlinear differential equations

In this paper, we prove an existence theorem for time global monotone positive solutions of nonlinear second-order ordinary differential equations by applying the Schauder-Tikhonov fixed point theorem. This result generalizes the result of existence on a half-line given in Yin (2003) [8].     

New fixed point theorems for <Emphasis Type="Italic">P</Emphasis><Subscript>1</Subscript>-compact mappings in Banach spaces

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.