拓扑空间中一些新的不动点定理

介绍了我们在不动点定理方面的一些最新结果，包括：拓扑空间中Meir-Keeler型映象的不动点定理，有序拓扑空间中增算子和多值增映射的不动点定理，拓扑空间中压缩映象的不动点定理和多值映象的公共不动点定理。甚至在通常的度量空间，所有这些结果也是新的。     

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i(A,Ω, p) is equal to nonzero, where i(A,Ω, p) is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point the-orems of the completely continuous and weakly inward mapping, which generalize...     

拓扑空间中Fan-Browder映射的连续选择定理及其应用

首先,在不具有任何凸性结构的拓扑空间中引入Fan-Browder映射的概念．然后,证明了一个新的关于Fan-Browder映射的连续选择定理,其中定义域是非紧的,值域是不具有任何凸性结构的拓扑空间的子集．作为应用,给出了一些不动点定理、叠合点定理和一个非空交定理．这些新的概念和定理统一和推广了许多已有的结果．     

Fixed points for weakly inward mappings in Banach spaces

S. Hu and Y. Sun [S. Hu, Y. Sun, Fixed point index for weakly inward mappings, J. Math. Anal. Appl. 172 (1993) 266-273] defined the fixed point index for weakly inward mappings, investigated its properties and studied the fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we continue to investigate boundary conditions, under which the fixed point index for the completely continuous and weakly inward mapping, denoted by i(A,Ω,P), is equal to 1 or 0. Correspondingly, we can obtain some new fixed point theorems of the completely continuous and weakly inward mappings and existence theorems of solutions for the equations Ax=μx, which extend many famous theorems such as Leray-Schauder's theorem, Rothe's two theorems, Krasnoselskii's theorem, Altman's theorem, Petryshyn's theorem, etc., to the case of weakly inward mappings. In addition, our conclusions and methods are different from the ones in many recent works.     

Banach空间中的广义Schauder基和广义A-proper映射的广义拓扑度

本文给出Banach空间中广义Schauder基的新概念及其几个性质定理,举出了具有广义Schauder基的不可分Banach空间实例。作为广义Schauder基的应用,还推广了A-proper映射的广义拓扑度和一些著名的不动点定理。     

af的拓扑度及其应用

本文首先对Rⁿ中连续映象讨论了af(a≠0)与f的Brouwer度之间的关系,得到了Brou-wer度的几个等式,顺便推出几个不动点定理.在此基础上研究了投影完备的实Banach空间中A-proper映象f与af的广义拓扑度之间的联系.作为应用,推广了关于P₁紧映象的Altman不动点定理.     

Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications

The purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, the monotone hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article modify and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257-266] and the results of Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007) 103-115] and the results of Su et al. [Y. Su, Z. Wang and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009) 5616-5628], and many others.     

A Fixed Point Theorem for Multi—valued Composite Increasing Operators

Ａ　Ｆｉｘｅｄ　Ｐｏｉｎｔ　Ｔｈｅｏｒｅｍ　ｆｏｒ　Ｍｕｌｔｉ－ｖａｌｕｅｄ　Ｃｏｍｐｏｓｉｔｅ　Ｉｎｃｒｅａｓｉｎｇ　ＯｐｅｒａｔｏｒｓＬｉＦｅｎｇｙｏｕ（李凤友）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｔｉａｎｊｉｎ＇ＮｏｒｍａｌＵｎｉ...     

拓扑度的一个性质

本建立了拓扑度的一个性质，即拓扑度的容斥性，并提出了一个不动点定理。     

Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings

In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are extensions of the well-known Nadler's fixed point theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-487], as well as of some Caristi type theorems for multi-valued operators, see [N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; J.P. Aubin, Optima and Equilibria. An Introduction to Nonlinear Analysis, Grad. Texts in Math., Springer-Verlag, Berlin, 1998, p. 17; S.S. Zhang, Q. Luo, Set-valued Caristi fixed point theorem and Ekeland's variational principle, Appl. Math. Mech. 10 (2) (1989) 111-113 (in Chinese), English translation: Appl. Math. Mech. (English Ed.) 10 (2) (1989) 119-121], etc.     

Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings

The purpose of this article is to prove strong convergence theorems for common fixed points of two closed hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, the monotone hybrid algorithms are presented and are used to approximate the common fixed points. Finally, a new simplified hybrid algorithm has been proposed and relative convergence theorem has been proved by using the new method for proofs. The results of this article modify and improve the results of Matsushita, Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257–266] and the results of Plubtieng, Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007) 103–115], and many others.     

Some common fixed point theorems for weakly compatible mappings

Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771-779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247-1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] is generalized and improved.     

Topological degree for 1-set-contractive fields in M-PN spaces and its applications

In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.     

Continuous Selection, Collectively Fixed Points and System of Coincidence Theorems in Product Topological Spaces

Some new continuous selection theorems are first proved in noncompact topological spaces. As applications, some new collectively fixed point theorems and coincidence theorems for two families of set-valued mappings defined on product space of noncompact topological spaces are obtained under very weak assumptions. These results generalize many known results in recent literature.     

Z—P—S空间中一类新的不动点定理

利用概率度量空间中A—proper映射拓扑度的基本性质,在投影完备的Z—P—S空间中研究了非线性映射的不动点问题,得到了一些新的结果．     

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].     

THE LERAY-SCHAUDER CONDITION FOR 1-SET WEAKLY-CONTRACTIVE AND （ws）-COMPACT OPERATORS

Abstract The main purpose of this article is to prove a collection of new nxea point theorems for （ws）-compact and so-called 1-set weakly contractive operators under Leray- Schauder boundary condition. We also introduce the concept of semi-closed operator at the origin and obtain a series of new fixed point theorems for such class of operators. As consequences, we get new fixed point existence for （ws）-compact （in particular nonexpansive） self mappings unbounded closed convex subset of Banach spaces. The main condition in our results is formulated in terms of axiomatic measures of weak noncompactness. Later on, we give an application to generalized Hammerstein type integral equations.     

Edelstein's method and fixed point theorems for some generalized nonexpansive mappings

A new condition for mappings, called condition (C), which is more general than nonexpansiveness, was recently introduced by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. Following the idea of Kirk and Massa Theorem in [W.A. Kirk, S. Massa, Remarks on asymptotic and Chebyshev centers, Houston J. Math. 16 (1990) 364-375], we prove a fixed point theorem for mappings with condition (C) on a Banach space such that its asymptotic center in a bounded closed and convex subset of each bounded sequence is nonempty and compact. This covers a result obtained by Suzuki [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095]. We also present fixed point theorems for this class of mappings defined on weakly compact convex subsets of Banach spaces satisfying property (D). Consequently, we extend the results in [T. Suzuki, Fixed point theorems and convergence theorems for some generalized nonexpansive mappings, J. Math. Anal. Appl. 340 (2008) 1088-1095] to many other Banach spaces.     

Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces

We introduce the concept of a mixed g-monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. Presented theorems are generalizations of the recent fixed point theorems due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393] and include several recent developments.     

拟-A-Proper映射的拓扑度

拓扑度理论为研究非线性方程多解问题提供了强有力的工具。迄今拓扑度方法已成为非线性泛函分析中最基本的方法之一(关于非线性泛函分析的发展近况请见田方增[1])。 本文提出很广泛的拟-A-proper映射类,用A-proper映射([5])逼近拟-A-proper映射的方法(类似[2])建立了后者的拓扑度;证明出两类映射拓扑度的性质几乎全同;讨论