A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES

Recently, Suzuki [T. Suzuki characterizes metric completeness, Proc. A generalized Banach contractlon principle that Amer. Math. Soc. 136 （2008）, 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char- acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki＇s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 （2012）, 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric O- completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.     

Common fixed point theorems for three maps in discontinuous Gb metric spaces

In [Aghajani A, Abbas M, Roshan JR. Common fixed point of generalized weak contractive mappings in partially ordered G_b-metric spaces. Filomat, 2013, in press], using the concepts of G-metric and b-metric Aghajani et al. defined a new type of metric which is called generalized b-metric or G_b-metric. In this paper, we prove a common fixed point theorem for three mappings in G_b-metric space which is not continuous. An example is presented to verify the effectiveness and applicability of our main result.     

Some new extensions of Edelstein-Suzuki-type fixed point theorem to G-metric and G-cone metric spaces

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74–79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.     

偏锥b-度量空间中的不动点定理

在偏锥度量空间的基础上,介绍了偏锥b-度量空间的相关概念,提出了偏锥b-度量空间和锥b-度量空间的关系,并给出了一个简单的例子,最后研究了偏锥b-度量空间中在没有正规性的条件下的一些不动点定理,从而推广了巴拿赫压缩原理.     

G-度量空间中两对非相容映象的几个新的公共不动点定理

在G-度量空间的框架下,利用自映象对的非相容性和（Ag）型R-弱交换性条件,在既不要求空间的完备性,也不要求映象连续的条件下,建立了一类？-压缩条件下的4个映象的几个新的公共不动点定理,此定理在很大程度上改进和发展了已有文献的相关结果.     

The matching theorems in G-convex spaces with applications

The purpose of this paper is to establish some new matching theorems in G-convex spaces and, as applications, to obtain some new fixed point theorems, section theorems and a minimax theorem in G-convex spaces. The results presented in this paper improve and generalize the corresponding results in [1], [2], [3], [4], [5], [7], [8], [9], [10], [11] and [12].     

赋值Banach代数的偏序D^-度量空间和公共不动点定理

基于完备的D^*-度量空间,提出具有Banach代数的偏序D^*-度量空间的定义,通过迭代序列的构造,证明了新定义下不动点定理的存在性及唯一性理论.随后引入了关于两个连续自映射的公共不动点定理,并对其存在性和唯一性进行了研究.所得结果推广了现有文献.     

On the location of fixed points on pairs of spaces

Let f: (X, A)→(X, A) be an admissible selfmap of a pair of metrizable ANR's. A Nielsen number of the complement Ñ(f; X, A) and a Nielsen number of the boundary ñ(f; X, A) are defined. Ñ(f; X, A) is a lower bound for the number of fixed points on C1(X - A) for all maps in the homotopy class of f. It is usually possible to homotope f to a map which is fixed point free on Bd A, but maps in the homotopy class of f which have a minimal fixed point set on X must have at least ñ(f; X, A) fixed points on Bd A. It is shown that for many pairs of compact polyhedra these lower bounds are the best possible ones, as there exists a map homotopic to f with a minimal fixed point set on X which has exactly Ñ(f; X - A) fixed points on C1(X−A) and ñ(f; X, A) fixed points on Bd A. These results, which make the location of fixed points on pairs of spaces more precise, sharpen previous ones which show that the relative Nielsen number N(f; X, A) is the minimum number of fixed points on all of X for selfmaps of (X, A), as well as results which use Lefschetz fixed point theory to find sufficient conditions for the existence of one fixed point on C1(X−A).     

Proximal point algorithm for nonlinear multivalued type mappings in Hadamard spaces

In this paper, we modify the proximal point algorithm for finding common fixed points in CAT(0) spaces for nonlinear multivalued mappings and a minimizer of a convex function and prove Δ‐convergence of the proposed algorithm. A numerical example is presented to illustrate the convergence result. Our results improve and extend the corresponding results in the literature.     

A Maurey type result for operator spaces

The little Grothendieck theorem for Banach spaces says that every bounded linear operator between C(K) and ?₂ is 2-summing. However, it is shown in [M. Junge, Embedding of the operator space OH and the logarithmic ‘little Grothendieck inequality’, Invent. Math. 161 (2) (2005) 225-286] that the operator space analogue fails. Not every cb-map is completely 2-summing. In this paper, we show an operator space analogue of Maurey's theorem: every cb-map is (q,cb)-summing for any q>2 and hence admits a factorization ‖v(x)‖?c(q)‖vcb_‖‖axbq_‖ with a,b in the unit ball of the Schatten class S2q.     

Fixed point theory for extension type maps in topological spaces

Several new fixed point results for self maps in extension type spaces are presented in this article.     

Deterministic and random fixed points for maps on extension type spaces

We present a variety of deterministic and random fixed point results for very general spaces and classes of maps.     

A new type of fixed point theorem in metric spaces

We prove a generalization of Edelstein’s fixed point theorem. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem.     

A fixed point result in Menger spaces using a real function

The main result of this paper is a fixed point theorem of self-mappings in Menger spaces which satisfy certain inequality. This inequality involves a class of real functions which we call Φ-functions. As a corollary we obtain a result in the corresponding metric spaces. The result is supported by an example. The class of real functions we have used is the conceptual extension of altering distance functions used in metric fixed point theory.      

Sobolev type spaces in quantum calculus

In this paper q-Sobolev type spaces are defined on Rq by using the q-cosine Fourier transform and its inverse. In particular, embedding results for these spaces are established. Next we define the q-cosine potential and study some of its properties.     

Fuzzy度量空间中的单值映射的Caristi型不动点定理

本文采用Ｋａｌａｖａ和Ｓｅｉｋｋａｌａ的模糊度量空间定义，利用文（７）中建立的亚度量簇生成空间理论，研究了Ｆｕｚｚｙ度量空间中的单值映射的Ｃａｒｉｓｔｉ型不动点定理以及它在Ｍｅｎｇｅｒ概率度量空间中的应用。     

New characterizations of Besov and Triebel-Lizorkin spaces over spaces of homogeneous type

Using the T1 theorem for the Besov and Triebel-Lizorkin spaces, we give new characterizations of Besov and Triebel-Lizorkin spaces with minimum regularity and cancellation conditions over spaces of homogeneous type.     

Unique common fixed point of a family of self-maps with same type contractive condition in 2-metric space

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if (i) {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; (ii) Tm,μ· Tn,ν = Tn,ν· Tm,μ for all m,n,μ,ν∈ N with μ = ν. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.     

On the Additivity of the Minkowski Functionals

In this work, we investigate the additivity of the Minkowski functionals associated to a cone in a linear vector space. As an application we discuss the equivalence of the classical Caristi fixed point theorem in metric spaces and its vectorial version in cone metric spaces.