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].     

Generalized cyclic contractions in partially ordered metric spaces

Abkar and Gabeleh in (J. Optim. Theory. Appl. doi:10.1007/s10957-011-9818-2) proved some theorems which ensure the existence and convergence of fixed points, as well as best proximity points for cyclic mappings in ordered metric spaces. In this paper we extend these results to generalized cyclic contractions and obtain some new results on the existence and convergence of fixed points for weakly contractive mappings, as well as on best proximity points for cyclic ??-contraction mappings in partially ordered metric spaces.     

TVS-值锥度量空间上拟-Lipschitz型映射族的公共不动点

在TVS-值锥度量空间上给出若干可数个满足拟-Lipschitz条件的满映射族的唯一公共不动点的存在性定理.主要结论推广和改进了文献中的一些相应结论.     

Unique Common Fixed Point for a Family of Mappings with a Nonlinear Quasi-Contractive Type Condition in Metrically Convex Spaces

A class Φ of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a φiquasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.     

Fixed point theorems for multi-valued contractions in complete metric spaces

In this paper the concept of a contraction for multi-valued mappings in a metric space is introduced and the existence theorems for fixed points of such contractions in a complete metric space are proved. Presented results generalize and improve the recent results of Y. Feng, S. Liu [Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103-112], D. Klim, D. Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132-139] and several others. The method used in the proofs of our results is new and is simpler than methods used in the corresponding papers. Two examples are given to show that our results are genuine generalization of the results of Feng and Liu and Klim and Wardowski.     

Fixed points, selections and common fixed points for nonexpansive-type mappings

We study the existence of fixed points in the context of uniformly convex geodesic metric spaces, hyperconvex spaces and Banach spaces for single and multivalued mappings satisfying conditions that generalize the concept of nonexpansivity. Besides, we use the fixed point theorems proved here to give common fixed point results for commuting mappings.     

On coincidence points of multivalued vector mappings of metric spaces

The notion of metric regularity can be extended to multivalued mappings acting in the products of metric spaces. A vector analog of Arutyunov’s coincidence-point theorem for two multivalued mappings is proved. Statements on the existence and estimates of solutions of systems of inclusions of special form occurring in the multiple fixed-point problem are obtained. In particular, these results imply some well-known double-point theorems.     

Common fixed points of almost generalized contractive mappings in ordered metric spaces

The existence theorems of common fixed points for two weakly increasing mappings satisfying an almost generalized contractive condition in ordered metric spaces are proved. Some comparative example are constructed which illustrate the values of the obtained results in comparison to some of the existing ones in literature.     

Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces

In this paper, we introduce the concept of tripled fixed point for nonlinear mappings in partially ordered complete metric spaces and obtain existence, and existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent coupled fixed point theorems established by Gnana Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 1379-1393]. Examples to support our new results are given.     

Points of Coincidence and Common Fixed Points for Ⅱ-Expansive Mappings on Complex Valued Metric Spaces

We use the two mappings satisfying Ⅱ-expansive conditions on complex valued metric spaces to construct the convergent sequences and prove that the unique limit of the sequences is the point of coincidence or common fixed point of the two mappings.Also,we discuss the uniqueness of points of coincidence or common fixed points and give the existence theorems of unique fixed points.The obtained results generalize and improve the corresponding conclusions in references.     

Generalized Probabilistic Metric Spaces and Fixed Point Theorems

Several results concerning generalized probabilistic spaces, fixed points of mappings on topological spaces are obtained and applied to yield some new theorems on fixed points for mappings on generalized probabilistic metric spaces.     

Coefficient bounds for biholomorphic mappings which have a parametric representation

The main purpose of this paper is to prove a collection of new fixed point theorems for so-called weakly F-contractive mappings. By analogy, we introduce also a class of strongly F-expansive mappings and we prove fixed point theorems for such mappings. We provide a few examples, which illustrate these results and, as an application, we prove an existence and uniqueness theorem for the generalized Fredholm integral equation of the second kind. Finally, in Appendix A, we apply the Mönch fixed point theorem to prove two results on the existence of approximate fixed points of some continuous mappings.     

Neumann p-Laplacian problems with a reaction term on metric spaces

We use a variational approach to study existence and regularity of solutions for a Neumann p-Laplacian problem with a reaction term on metric spaces equipped with a doubling measure and supporting a Poincaré inequality. Trace theorems for functions with bounded variation are applied in the definition of the variational functional and minimizers are shown to satisfy De Giorgi type conditions.

     

度量凸空间上非自映射族的唯一公共不动点定理

给出了若干个度量凸空间的闭子集上的非自映射族的公共不动点的存在性与唯一性.我们的主要结果对文献中的许多同类型的不动点定理进行了改进和一般化.     

Some fixed point theorems for multivalued mappings concerning <Emphasis Type="Italic">F</Emphasis>-contractions

The aim of this paper is to prove some fixed point theorems for multivalued maps satisfying different inequalities based on Wardowski’s technique in complete metric spaces. Our results extend and generalize several known results in the literature. We also give an application to the existence of fixed points for a class of Lipschitz multivalued mappings with a constant being greater than 1. Examples are also given to illustrate our results.     

Fixed point theorems for set-valued contractions in complete metric spaces

The fixed point theory of set-valued contractions which was initiated by Nadler [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969) 475-488] was developed in different directions by many authors, in particular, by [S. Reich, Fixed points of contractive functions, Boll. Unione Mat. Ital. 5 (1972) 26-42; N. Mizoguchi, W. Takahashi, Fixed point theorems for multivalued mappings on complete metric spaces, J. Math. Anal. Appl. 141 (1989) 177-188; Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103-112]. In the present paper, the concept of contraction for set-valued maps in metric spaces is introduced and the conditions guaranteeing the existence of a fixed point for such a contraction are established. One of our results essentially generalizes the Nadler and Feng-Liu theorems and is different from the Mizoguchi-Takahashi result. The second result is different from the Reich and Mizoguchi-Takahashi results. The method used in the proofs of our results is inspired by Mizoguchi-Takahashi and Feng-Liu's ideas. Comparisons and examples are given.     

On coincidence points for vector mappings

For mappings acting in the product of metric spaces we propose a concept of vector covering. This concept is a natural extension of the notion of covering formappings inmetric spaces. The statements on the solvability of systems of operator equations are proved for the case when the left-hand side of an equation is a value of a vector covering mapping and the right-hand side is Lipschitzian vector mapping. In the scalar case the obtained statements are equivalent to the coincidence point theorems by A. V. Arutyunov. As an application, we prove a statement on the existence of n-fold coincidence points and obtain estimates of the points. The sufficient conditions for n-fold fixed points existence, including the well-known theorems on double fixed point, follow from the obtained results.     

M-PM空间中反交换映像的公共不动点定理

在M-PM空间中引入了反交换映像的概念,并讨论了映像在反交换条件下的公共不动点的存在性及唯—性问题,同时将此结果推广到Fuzzy度量空间中,改进和推广了若干重要结论.     

复值度量空间上的B-隐式压缩条件和唯一(公共)不动点（英文）

A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.     

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.