A New Form of Fuzzy Compact Spaces and Related Topics via Fuzzy Idealization

Fuzzy ideals and the notion of fuzzy local function were introduced and studied by Sarkar[12] and by Mahmoud in [9]. The purpose of this paper deals with a fuzzy compactness modulo a fuzzy ideal. Many new sorts of weak and strong fuzzy compactness have been introduced to fuzzy topological spaces in the last twenty years but not have been studied using fuzzy ideals so,the main aim of our work in this paper is to define and study some new various types of fuzzy compactness with respect to fuzzy ideals namely fuzzy L-compact and L*-compact spaces. Also fuzzy compactness with respect to ideal is useful as unification and generalization of several others widely studied concepts. Possible application to superstrings and E∞ space-time are touched upon.     

On p-convergent Operators on Banach Lattices

The notion of a p-convergent operator on a Banach space was originally introduced in 1993 by Castillo and S′anchez in the paper entitled "Dunford–Pettis-like properties of continuous vector function spaces". In the present paper we consider the p-convergent operators on Banach lattices, prove some domination properties of the same and consider their applications(together with the notion of a weak p-convergent operator, which we introduce in the present paper) to a study of the Schur property of order p. Also, the notion of a disjoint p-convergent operator on Banach lattices is introduced, studied and its applications to a study of the positive Schur property of order p are considered.     

超拟群的模糊正则关系

Regular relations play in hyperquasigroups theory a role analogous to congruences in semigroup theory.The aim of this paper is to introduce the concept of regular relations on hyperquasigroups and to investigate some related properties.Further,the notion of fuzzy regular relations on hyperquasigroups is introduced and some characterizations are discussed.     

双极值模糊集在半环上的应用

On the basis of concepts of bipolar fuzzy sets, we establish a new framework of bipolar fuzzy subsemirings（resp., ideals） which is a generalization of traditional fuzzy subsemirings（resp., ideals） in semirings. The concepts of bipolar fuzzy subsemirings（resp., ideals） are introduced and related properties are investigated by means of positive t-cut, negative s-cut and equivalence relation. Particularly, the notion of a normal bipolar fuzzy ideal is given, and some basic properties are studied in this paper.     

CHARACTER, DENSITY AND CELLULARITY OF L-FUZZY TOPOLOGICAL SPACES

In this paper we generalize the notions of weight,character, density and cellularity of topological spaces to L-fuzzy topogical spaces. We prove theorems corresponding to some of usual theorems. In particular we generalize Hewitt-Marczewski-Pondiczery theorem on the density of the product of topological spaces to the case of L-fuzzy topological spaces (Theorem 4. 4). We also discuss the relations between topological spaces and its induced fuzzy topological spaces for these cardinal functions.     

Weighted Best Local Approximation

In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the Lp spaces and recent results in Orlicz spaces.The notion of balanced point,introduced by Chui et al.in 1984 are extensively used.     

(α,β)-fuzzy Subalgebras of Q-algebras

In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets,the notion of (α,β)-fuzzy Q-algebras,the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q.Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras.The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined,and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.     

SOME EULER SPACES OF DIFFERENCE SEQUENCES OF ORDER m

Kizmaz [13] studied the difference sequence spaces e∞(△), c(△), and c0(△).Several article dealt with the sets of sequences of m-th order difference of which are bounded, convergent, or convergent to zero. Altay and Basar [5] and Altay, Basar, and Mursaleen [7] introduced the Euler sequence spaces eτ0, eτ0, andeτ∞, respectively. The main purpose of this article is to introduce the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)) consisting of all sequences whose mth order differences are in the Euler spaces eτ0, eτc, and eτ∞, respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the α-, β-, and γ-duals of the spaces eτ0(△(m)), eτc(△(m)), and eτ∞(△(m)), and the Schauder basis of the spaces eτ0(△(m)), eτc(△(m)). The last section of the article is devoted to the characterization of some matrix mappings on the sequence space eτc(△(m)).     

A SUFFICIENT CONDITION FOR K-SMOOTH SPACES

The notion of K-Smooth space was introduced in a recent paper.Thepurpose of this paper is to give a sufficient condition for K-Smooth spaces,which will generalize a theorem of Chen Daoqi on a sufficient conditionfor the uniqueness of support functional.     

THE BOUNDEDNESS OF SOME INTEGRAL OPERATORS IN A NEW CLASS OF FUNCTION SPACES

A new class of function spaces, denoted by Ba, was introduced in [1]. It includes not only some familiar Orlicz spaces, Orlicz-Sobolev spaces but also some useful new function spaces. Ba spaces have gotten many applications (see, for example,[1-3]). In this paper, we discuss the boundedness of some well-known integral operators in space (L_(p_m),,a_m), which is a significant special case of Ba.     

α-FUZZY PAIRWISE RETRACT OF L-VALUED PAIRWISE STRATIFICATION SPACES

The notion of a fuzzy retract was introduced by Rodabaugh (1981). The notion of a fuzzy pairwise retract was introduced in 2001. Some weak forms and some strong forms of α-continuous mappings were introduced in 1988 and 1997. The authors extend some of these forms to the L-fuzzy bitopological setting and construct various α-fuzzy pairwise retracts. The concept of weakly induced spaces in the case L = [0, 1] was introduced by Martin (1980). Lin and Luo (1987) generalized this notion to the case that L is an arbitrary F-lattice and introduced the notion of induced L-fts. Several results are obtained, especially, for L-valued pairwise stratification spaces.     

q-一致光滑和严格凸的Banach空间中的无穷个严格伪压缩映射的混合迭代算法

在q-一致光滑和严格凸的Banach空间中,研究了无穷个严格伪压缩映射的混合迭代算法,证明了由这种新的算法产生的序列强收敛于这无穷个严格伪压缩映射的公共不动点,并且是变分不等式〈(I-A)x,J_q(p-x)〉≤0,p∈(n i=l)F(T_i)的解.论文推广和改进了一些前人的相应结论.     

关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记

D.M. Speegle 在文献[1] 中给出了具有常数 $\alpha$的性质${\cal A}$ 的定义,并且证明了任意无限维的可分一致光滑Banach空间都具有这样的性质,而且常数 $\alpha\in [0,1)$.本文给出了一个使得无限维可分Banach空间具有这种性质的充分条件,以及几个关于文献[1] 的注解.     

$\mathcal{F}$-Perfect Rings and Modules

Let $R$ be a ring, and let $(\mathcal{F}, C)$ be a cotorsion theory. In this article, the notion of $\mathcal{F}$-perfect rings is introduced as a nontrial generalization of perfect rings and A-perfect rings. A ring $R$ is said to be right $\mathcal{F}$-perfect if $F$ is projective relative to $R$ for any $F ∈ \mathcal{F}$. We give some characterizations of $\mathcal{F}$-perfect rings. For example, we show that a ring $R$ is right $\mathcal{F}$-perfect if and only if $\mathcal{F}$-covers of finitely generated modules are projective. Moreover, we define $\mathcal{F}$-perfect modules and investigate some properties of them.     

Some new sequence spaces derived by The composition of binomial matrix and double band matrix

In this paper, we construct three new sequence spaces $b^{{r,s}}_{0}(G)$, $b^{{r,s}}_{c}(G)$ and $b^{{r,s}}_{\infty}(G)$ and mention some inclusion relations, where $G$ is generalized difference matrix. Moreover, we give Schauder basis of the spaces $b^{{r,s}}_{0}(G)$ and $b^{{r,s}}_{c}(G)$. Afterward, we determine $\alpha-$, $\beta-$ and $\gamma-$duals of those spaces. Finally, we characterize some matrix classes related to the space $b^{{r,s}}_{c}(G)$.     

$\mathbb{Z}^{k}$-作用一维子系统的Lipschitz跟踪性

本文主要研究了$\mathbb{Z}^{k}$-作用一维子系统的跟踪性质. 文中运用两种等价的方式引入了$\mathbb{Z}^{k}$-作用一维子系统的伪轨以及跟踪性的概念. 对于一个闭黎曼流形上的光滑$\mathbb{Z}^{k}$-作用$T$, 我们通过诱导的非自治动力系统提出了Anosov方向的概念. 借助Bowen几何的方法, 我们证明了$T$沿着任意Anosov方向具有Lipschitz跟踪性.     

赋$\beta$-范空间中的最佳逼近问题

本文讨论赋$\beta$-范空间中的最佳逼近问题.以[1]引进的共轭锥为工具,借助[2]中关于$\beta$-次半范的Hahn-Banach延拓定理,第二节给出赋$\beta$-范空间的闭子空间中最佳逼近元的特征,第三节得到赋$\beta$-范空间中任何凸子集或子空间均为半Chebyshev集的充要条件是空间本身严格凸,文章最后证明了严格凸的赋$\beta$-范空间中任何有限维子空间都是Chebyshev集.     

权重$l_2$空间上关联线性时不变算子的性质

本文讨论了选取不同类型权重序列$\{w(t)\}_{t\in \mathbb{Z}}$时,权重$l_2(\mathbb{Z},w)$空间上关联线性时不变算子的性质,同时还讨论了非稳定关联线性时不变卷积算子的可闭性的有关问题,提出了关于线性时不变算子一些新的问题,并指出可在一大类权重$l_2(\mathbb{Z},w)$空间上进行鲁棒设计.     

Stability of disjointness preserving mappings

Let and be compact Hausdorff spaces and let . A linear mapping is called -disjointness preserving if implies that . If is a continuous or surjective -disjointness preserving linear mapping, we prove that there exists a disjointness preserving linear mapping satisfying . We also prove that every unbounded -disjointness preserving linear functional on is disjointness preserving.

     

Spaces of type BLO for non-doubling measures

The spaces of type BLO for the positive Radon measures satisfying a growth condition on are introduced. It is shown that some properties which hold for the classical space BLO when is a doubling measure remain valid for the spaces of type BLO introduced in this paper, without assuming doubling.