Covering maps of spaces of compact subsets

Mappings generated by covering maps of metric spaces are considered in the spaces of compact subsets of metric spaces. Sufficient conditions for the covering property of maps of spaces of compact sets and sufficient conditions for the existence of coincidence sets of maps of metric spaces are obtained.     

Inclusion properties of generalized Morrey spaces

This paper discusses the structure of Morrey spaces, weak Morrey spaces, generalized Morrey spaces, and generalized weak Morrey spaces. Some necessary and sufficient conditions for the inclusion property of these spaces are obtained through a norm estimate for the characteristic functions of balls.     

Exponential homeomorphisms in the category of topological spaces with base point

Topologies on base point preserving function spaces are studied making use of the Brown-Booth-Tillotson C-smash product and the topologies on function spaces defined by the classes C of exponentiable spaces. Some conditions on the classes C are obtained for exponential bijections and exponential homeomorphisms in the category of topological spaces with base point. Conditions for exponential homeomorphisms are obtained for CW-complexes whose cellular structure implies precise results.     

Net Spaces and Boundedness of Integral Operators

In this paper we introduce new functional spaces which we call net spaces. Using their properties, necessary and sufficient conditions for the integral operators to be of strong or weak type are obtained. Estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.     

Musielak-Orlicz序列空间中的S-点

本文给出了Musielak-Orlicz序列空间中S-点的充要判别准则.作为推论,得到Musielak-Orlicz序列空间具有S-性质的充分必要条件.     

乘积Banach空间中等式约束向量极值问题的最优性必要条件

本文利用Banach空间中的隐函数定理和序线性拓扑空间中对于次似凸向量值映射的择一定理,得出了乘积Banach空间中具有等式约束向量极值问题的若干最优性必要条件.     

On a Priori Estimates and Fredholm Property of Differential Operators in Anisotropic Spaces

The paper is devoted to special a priori estimates and Fredholm property of differential operators acting in anisotropic Sobolev spaces in ?ⁿ. Necessary conditions for a priori estimates in terms of the symbol of an operator are obtained. Under appropriate conditions imposed on the coefficients, a priori estimates are obtained in the corresponding weighted spaces.     

Disjointly strictly singular inclusions of symmetric spaces

In this paper, the disjoint strict singularity of inclusions of symmetric spaces of functions on an interval is considered. A condition for the presence of a “gap” between spaces sufficient for the inclusion of one of these spaces into the other to be disjointly strictly singular is found. The condition is stated in terms of fundamental functions of spaces and is exact in a certain sense. In parallel, necessary and sufficient conditions for an inclusion of Lorentz spaces to be disjointly strictly singular (and similar conditions for Marcinkiewicz spaces) are obtained and certain other assertions are proved. Translated fromMatematicheskie Zametki, Vol. 65, No. 1, pp. 3–14, January, 1999.     

Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds

This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.     

Approximate controllability of semilinear functional equations in Hilbert spaces

In this paper approximate and complete controllability for semilinear functional differential systems is studied in Hilbert spaces. Sufficient conditions are established for each of these types of controllability. The results address the limitation that linear systems in infinite-dimensional spaces with compact semigroup cannot be completely controllable. The conditions are obtained by using the Schauder fixed point theorem when the semigroup is compact and the Banach fixed point theorem when the semigroup is not compact.     

Topological characterizations of linearly uniformizable spaces

The spaces having uniformities with a totally ordered base are characterized in bigger classes of non-archimedean spaces and suborderable spaces. Consequently, several new metrization results are obtained. By examples, we show that the conditions used in our main theorem cannot be weakened essentially. Our examples may be interesting elsewhere, too.     

Some Estimates of Bilinear Hausdorff Operators on Stratified Groups

In this paper, we give four kinds of sharp estimates of two variants of bilinear Hausdorff operators on stratified groups, involving weighted Lebesgue spaces, classical Morrey spaces and central Morrey spaces. Meanwhile, some necessary and sufficient conditions of boundness are obtained.     

Fixed point theorems for a class of nonlinear operators in Banach spaces and applications

In this paper, we study a class of nonlinear operator equations with more extensive conditions in ordered Banach spaces. By using the cone theory and Banach contraction mapping principle, the existence and uniqueness of solutions for such equations are investigated without demanding the existence of upper and lower solutions and compactness and continuity conditions. The results in this paper are applied to a class of abstract semilinear evolution equations with noncompact semigroup in Banach spaces and the initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces. The results obtained here improve and generalize many known results.     

The Solvability of Nonlinear Split Ordered Variational Inequality Problems in Partially Ordered Vector Spaces

The concept of nonlinear split ordered variational inequality problems on partially ordered Banach spaces extends the concept of the linear split vector variational inequality problems on Banach spaces, while the latter is a natural extension of vector variational inequality problems on Banach spaces. In this article, we prove the solvability of some nonlinear split vector variational inequality problems by using fixed-point theorems on partially ordered Banach spaces. It is important to notice that in the results obtained in this article, the considered mappings are not required to have any type of continuity and they just satisfy some order-monotonic conditions. Consequently, both the solvability of linear split vector variational inequality problems and vector variational inequality problems will be immediately obtained from the solvability of nonlinear split vector variational inequality problems. We will apply these results to solving nonlinear split vector optimization problems. The underlying spaces of the considered variational inequality problems may just be vector spaces which do not have topological structures, the considered mappings are not required to satisfy any continuity conditions, which just satisfy some order-increasing conditions.     

On the boundedness of operator generated by the Haar multishift

Boundedness conditions for operators generated by Haar multishifts in symmetric spaces with nontrivial Boyd indices are obtained.     

Correctness of general boundary-value problems in a half-space for differential equations with constant coefficients in the classes of functions of power growth and decay

We present the necessary and sufficient conditions of correctness of general boundary-value problems in a half-space for homogeneous differential equations with constant coefficients in the spaces of functions that have the exponential behavior at infinity in a separated variable and are rapidly decaying in the remaining variables. On their basis, we obtained the sufficient conditions of solvability of the indicated problems in the spaces of distributions of slow growth.     

On necessary conditions for the Fredholm solvability of nonlocal elliptic problems

Nonlocal elliptic problems in plane domains are considered. Necessary conditions for the Fredholm solvability of such problems in weighted spaces are obtained.     

Integral operators with homogeneous kernels in grand Lebesgue spaces

Sufficient conditions on the kernel and the grandizer that ensure the boundedness of integral operators with homogeneous kernels in grand Lebesgue spaces on ? ⁿ as well as an upper bound for their norms are obtained. For some classes of grandizers, necessary conditions and lower bounds for the norm of these operators are also obtained. In the case of a radial kernel, stronger estimates are established in terms of one-dimensional grand norms of spherical means of the function. A sufficient condition for the boundedness of the operator with homogeneous kernel in classical Lebesgue spaces with arbitrary radial weight is obtained. As an application, boundedness in grand spaces of the one-dimensional operator of fractional Riemann–Liouville integration and of a multidimensional Hilbert-type operator is studied.     

On extremal pure Nash equilibria for mixed extensions of normal-form games

In this paper we derive conditions under which mixed extensions of normal-form games have least and greatest Nash equilibria in pure strategies, and either of them gives best utilities among all mixed Nash equilibria when strategy spaces are complete separable metric spaces equipped with closed partial orderings, and the values of utility functions are in separable ordered Banach spaces. The obtained results are applied to supermodular normal-form games whose strategy spaces are multidimensional.     

Existence results for systems of vector variational-like inequalities

The purpose of this paper is to introduce and study systems of vector variational-like inequalities in Banach spaces. Under certain conditions, some existence results for systems of vector variational-like inequalities in Banach spaces are obtained by Kakutani–Fan–Glicksberg fixed point theorem.