Three fixed point theorems for generalized contractions with constants in complete metric spaces

We prove three fixed point theorems for generalized contractions with constants in complete metric spaces, which are generalizations of very recent fixed point theorems due to Suzuki. We also raise one problem concerning the constants.     

一般化凸乘积空间上Fan-Browder型不动点定理和平衡点定理

我们得到了一般化凸乘积空间上 Fan- Browder型不动点定理 ,然后利用上述结果给出 (部分 )极大元素和平衡点的存在定理     

Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces

Let X be a non-empty set and F:X×X→X be a given mapping. An element (x,y)∈X×X is said to be a coupled fixed point of the mapping F if F(x,y)=x and F(y,x)=y. In this paper, we consider the case when X is a complete metric space endowed with a partial order. We define generalized Meir-Keeler type functions and we prove some coupled fixed point theorems under a generalized Meir-Keeler contractive condition. Some applications of our obtained results are given. The presented theorems extend and complement the recent fixed point theorems due to Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006) 1379-1393].     

Bead spaces and fixed point theorems

The notion of a bead metric space defined here (see Definition 6) is a nice generalization of that of the uniformly convex normed space. In turn, the idea of a central point for a mapping when combined with the “single central point” property of the bead spaces enables us to obtain strong and elegant extensions of the Browder-Göhde-Kirk fixed point theorem for nonexpansive mappings (see Theorems 14-17). Their proofs are based on a very simple reasoning. We also prove two theorems on continuous selections for metric and Hilbert spaces. They are followed by fixed point theorems of Schauder type. In the final part we obtain a result on nonempty intersection.     

Iterative fixed point theorems in E-metric spaces

We present a multivalued nonlinear fixed point theorem in an E-metric space introducing the concept of strict positivity in a Riesz space. Our result extends some well-known fixed point theorems obtained by J. Matkowski, R. W?grzyk, R. Cristescu, and C. Çevik, I. Altun.     

Fixed point theorems in generalized Hilbert spaces

Some fundamental fixed point theorems are proved for locally convex spaces whose generating family of seminorms satisfies the parallelogram law.     

Coupled fixed point theorems in cone metric spaces

In this paper, by considering two metrics, we obtain some coupled fixed point theorems in cone metric spaces by assuming that the cone has nonempty interior as well as employing a number of contractive-type conditions. Our results generalize and extend some recently announced results in the literature.     

半序积空间中新的不动点定理

使用半序理论,h-序差和变距离函数的性质,在半序积Banach空间上讨论了一类没有凹凸性的单调算子,得出新的不动点存在唯一性结果,推广了文献中相关的不动点定理.     

Common fixed point theorems in probabilistic metric spaces

We extend the notion of R-weak commutativity and its variants to probabilistic metric spaces and prove common fixed point theorems concerning them. Examples are included to reflect upon the distinctiveness of the types of mappings defined in the paper.      

Some fixed point theorems in convex metric spaces

The concept of a convex metric space was introduced by Takahashi [10]. He observed that it is possible to generalize fixed point theorems in Banach spaces. Subsequently, Machado [8], Itoh [5], Naimpally, Singh and Whitfield [9] and Beg and Azam [2], among others have studied fixed point theorems in convex metric spaces. This paper is a continuation of these investigations.     

Fixed point theorems in new generalized metric spaces

The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi: 10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler–Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.     

Common fixed point theorems for four mappings through generalized altering distances in ordered metric spaces

Using the concepts introduced by Abbas et?al. (Appl Math Lett 24:1520?C1526, 2011), the purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions under generalized altering distance functions in ordered complete metric spaces.     

Common fixed point theorems in intuitionistic fuzzy metric spaces

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]).     

Some fixed point theorems in fuzzy reflexive Banach spaces

In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910–31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271–89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it’s topological structure. Chaos, Solitons & Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.     

Common fuzzy fixed point theorems in ordered metric spaces

We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contractive condition in complete ordered spaces. Our results provide extension as well as substantial improvements of several well-known results in the existing literature and initiate the study of fuzzy fixed point theorems in ordered spaces.     

KKM property and fixed point theorems in metric spaces

In this paper, first part, we establish some fixed point theorems for a k-set contraction map on the nearly-subadmissible subsets of a complete metric space. The second part, we deduce a generalization of the approximate fixed point theorem for the lower semicontinuous mappings on a metric space.     

Approximate fixed point theorems in Banach spaces with applications in game theory

In this paper some new approximate fixed point theorems for multifunctions in Banach spaces are presented and a method is developed indicating how to use approximate fixed point theorems in proving the existence of approximate Nash equilibria for non-cooperative games.     

Weak fixed point property for nonexpansive mappings with respect to orbits in Banach spaces

In this paper, we first show that a Banach space X has weak normal structure if and only if X has the weak fixed point property for nonexpansive mappings with respect to (wrt) orbits. Then, we give a counterexample to show that the Goebel–Karlovitz lemma does not hold for minimal invariant sets of nonexpansive mappings wrt orbits, and we present a modified version of the Goebel–Karlovitz lemma.