On explicit and implicit operator and differential inclusions in ordered spaces

In this paper we study solvability of inclusion problems in ordered topological vector spaces, and apply the obtained results to operator inclusions in ordered Banach spaces and to differential inclusions of explicit and implicit type.     

A fixed point theorem for multi-valued mappings and its applications to integral inclusions

In this paper we prove an existence theorem for the common solutions for a pair of integral inclusions via a common fixed point theorem of Dhage et al. [B.C. Dhage, D. O’Regan, R.P. Agarwal, Common fixed point theorems for a pair of countably condensing mappings in ordered Banach spaces, J. Appl. Math. Stoch. Anal. 16 (3) (2003) 243–248].     

取值于序拓扑向量空间的映射与层空间

In the paper [Monotone countable paracompactness and maps to ordered topological vector spaces, Top. Appl., 2014, 169(3): 51–70], Yamazaki initiated the study on maps with values into ordered topological vector spaces. Characterizations of monotonically countably paracompact spaces and some other spaces in terms of maps to ordered topological vector spaces were obtained. In this paper, following Yamazaki's method, we present some characterizations of stratifiable spaces and k-semi-stratifiable spaces in terms of maps with values into ordered topological vector spaces.     

拓扑序空间中的广义向量值均衡问题

利用一个KKM型定理,在拓扑序空间中,建立了关于广义向量值均衡问题解的某些新的存在性定理.     

对带误差项的Banach空间中完全广义集值拟变分包含的摄动迭代算法

研究了一类新的实Banach空间中的广义集值拟变分包含:f∈N(x，y) M(z，v) W(g(u)-h(w)，u)，它包含了近几年许多作者所作的变分包含同题．在买Banach空间中，利用极大增生算子的性质，建立了Banach空间中的广义集值拟变分包含和不动点问题间的等价性．利用这种等价性，建立了一些摄动迭代算法，并证明了近似解序列强收敛于精确解．本文的算法和结果改进和一般化了最近许多文章中相应的算法和结果。     

Banach空间中一类广义混合非线性隐拟变分包含解的三步迭代

本文引入并研究了实Banach空间中一类新的广义混合非线性隐拟变分包含 ,通过对实Banach空间中的m 增生映象运用Nadler定理和Michael选择定理 ,构建了这类新的广义变分包含解的三步迭代算法 ,并证明了其解的存在性和由迭代算法生成的迭代序列的收敛性     

Nonstandard hulls of ordered vector spaces

This paper undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated.     

Positive one-parameter semigroups on ordered banach spaces

In this review we describe the basic structure of positive continuous one-parameter semigroups acting on ordered Banach spaces. The review is in two parts.First we discuss the general structure of ordered Banach spaces and their ordered duals. We examine normality and generation properties of the cones of positive elements with particular emphasis on monotone properties of the norm. The special cases of Banach lattices, order-unit spaces, and base-norm spaces, are also examined.Second we develop the theory of positive strongly continuous semigroups on ordered Banach spaces, and positive weak^*-continuous semigroups on the dual spaces. Initially we derive analogues of the Feller-Miyadera-Phillips and Hille-Yosida theorems on generation of positive semigroups. Subsequently we analyse strict positivity, irreducibility, and spectral properties, in parallel with the Perron-Frobenius theory of positive matrices.     

Equivalent conditions for generalized contractions on (ordered) metric spaces

We establish a geometric lemma giving a list of equivalent conditions for some subsets of the plane. As its application, we get that various contractive conditions using the so-called altering distance functions coincide with classical ones. We consider several classes of mappings both on metric spaces and ordered metric spaces. In particular, we show that unexpectedly, some very recent fixed point theorems for generalized contractions on ordered metric spaces obtained by Harjani and Sadarangani [J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. 72 (2010) 1188-1197], and Amini-Harandi and Emami [A. Amini-Harandi, H. Emami A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. 72 (2010) 2238-2242] do follow from an earlier result of O’Regan and Petru?el [D. O’Regan and A. Petru?el, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008) 1241-1252].     

Monotone generalized contractions in partially ordered probabilistic metric spaces

In this paper, a concept of monotone generalized contraction in partially ordered probabilistic metric spaces is introduced and some fixed and common fixed point theorems are proved. Presented theorems extend the results in partially ordered metric spaces of Nieto and Rodriguez-Lopez [Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], Ran and Reurings [A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443] to a more general class of contractive type mappings in partially ordered probabilistic metric spaces and include several recent developments.     

Some general theorems on the existence of order-preserving functions

This paper proves some general theorems on the existence of order-preserving functions on topological ordered spaces. The proofs are based on Nachbin's generalization to topological ordered spaces of the theorems of Urysohn and Weil in general topology.     

Metrizably fibered generalized ordered spaces

In this paper we characterize generalized ordered spaces that are metrizably fibered in terms of certain quotient spaces and in terms of the existence of special open covers. We apply our results to give a new characterization of perfect generalized ordered spaces that have a σ-closed-discrete dense subset and to give examples of GO-spaces that are, or are not, metrizably fibered.     

A Completion Functor for Ordered Cauchy Spaces

A completion functor is constructed on a completion subcategory of the category of ordered CAUCHY spaces which preserves regularity, total boundedness, and uniformizability. Objects in the completion subcategory include the uniformizable ordered CAUCHY spaces and the c-embedded CAUCHY spaces with discrete order.     

A Brézis-Browder principle on partially ordered spaces and related ordering theorems

Through a simple extension of Brézis-Browder principle to partially ordered spaces, a very general strong minimal point existence theorem on quasi ordered spaces, is proved. This theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems, and three general Ekeland variational principles in optimization problems where the objective space is quasi ordered. Then, they are applied to prove strong minimal point existence results, generalizations of Bishop-Phelps lemma in linear spaces, and Ekeland variational principles in set-valued optimization problems through a set solution criterion.     

Topologies on totally ordered sets

A well-formed ordered space is a totally ordered set equipped with any topology which possesses a subbase consisting entirely of initial and final segments of the set. The well-formed ordered spaces are the structures obtained by repeatedly taking subspaces, quotient spaces and inverse limits, starting from a collection of totally ordered sets with the interval topology, and the paper studies their properties.     

κ-compactness,extent and the Lindelöf number in LOTS

We study the behaviour of ?-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.     

Quantifying Democracy of Wavelet Bases in Lorentz Spaces

We study the efficiency of the greedy algorithm for wavelet bases in Lorentz spaces in order to give the near best approximation. The result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces.     

线性空间中向量极值问题的最优性条件

文 [1]建立了线性拓扑空间中向量极值问题的广义 Kuhn- Tucker条件和 L agrange乘子存在定理 .本文将在线性空间中讨论这方面问题 ,首先在线性空间中建立了次似凸向量值映射的择一定理 ,进而得出序线性空间中向量极值问题的最优性条件及其标量化定理 .     

On stationary points of multivalued strongly contractive mappings in partially ordered ultrametric spaces and non-Archimedean

The purpose of this paper is to present a fixed point theorem for multivalued strongly contractive mappings in partially ordered ultrametric spaces. Also a consequence is obtained for these mappings in partially ordered non-Archimedean normed spaces. Finally, two supporting examples of these results are given.     

Characterizations of ultrabarrelledness and barrelledness involving the singularities of families of convex mappings

Summary The paper reveals that ultrabarrelled spaces (respectively barrelled spaces) can be characterized by means of the density of the so-called weak singularities of families consisting of continuous convex mappings that are defined on an open absolutely convex set and take values in a locally full ordered topological linear space (respectively locally full ordered locally convex space). The idea to establish such characterizations arose from the observation that, in virtue of well-known results, the density of the singularities of families of continuous linear mappings allows to characterize both the ultrabarrelled spaces and the barrelled spaces.