Related papers: Examples in Cone Metric Spaces: A Survey
We consider conformal deformations within a class of incomplete Riemannian metrics which generalize conic orbifold singularities by allowing both warping and any compact manifold (not just quotients of the sphere) to be the "link" of the…
We consider a new type of mappings in metric spaces which can be characterized as mappings contracting perimeters of triangles. It is shown that such mappings are continuous. The fixed-point theorem for such mappings is proved and the…
In this paper, we study different kinds of normal properties for infinite system of arbitrarily many convex sets in a Banach space and provide the dual characterization for the normal property in terms of the extended Jamenson property for…
This paper deals with functions that defined in metric spaces and valued in complete paranormed vector spaces or valued in Banach spaces, and obtains some necessary and sufficient conditions for weak convergence of finite measures.
Some examples of three-dimensional metrics of constant curvature defined by solutions of nonlinear integrable differential equations and their generalizations are constructed. The properties of Riemann extensions of the metrics of constant…
We discuss some open problems in the Geometry of Banach spaces having Ramsey-theoretic flavor. The problems are exposed together with well known results related to them.
We describe a construction (the `warped cone construction') which produces examples of coarse spaces with large groups of translations. We show that by this construction we can obtain many examples of coarse spaces which do not have…
We study homomorphisms on the algebra of analytic functions of bounded type on a Banach space. When the domain space lacks symmetric regularity, we show that in every fiber of the spectrum there are evaluations (in higher duals) which do…
We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $A\subseteq \mathbb{N}$ has positive Banach logarithmic density, then $A$ contains an approximate…
We study existence and partial regularity relative to the weighted Steiner problem in Banach spaces. We show $C^1$ regularity almost everywhere for almost minimizing sets in uniformly rotund Banach spaces whose modulus of uniform convexity…
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
We investigate a method for producing concrete convex-transitive Banach spaces. The gist of the method is in getting rid of dissymmetries of a given space by taking a carefully chosen quotient. The spaces of interest here are typically…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
It is shown that for every $k\in\mathbb{N}$ and every spreading sequence $\{e_n\}_{n\in\mathbb{N}}$ that generates a uniformly convex Banach space $E$, there exists a uniformly convex Banach space $X_{k+1}$ admitting…
We consider conformal metrics of constant curvature 1 on a Riemann surface, with finitely many prescribed conic singularities and prescribed angles at these singularities. Especially interesting case which was studied by C. L. Chai, C. S…
We introduce a generalization for bounded geometry that we call bounded scale measure. We show that bounded scale measure is a coarse invariant unlike bounded geometry. We then show equivalent definitions for spaces with bounded scale…
In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.
In this paper we study some basic properties of strong A-statistical convergence and strong A-statistical Cauchyness of sequences in probabilistic metric spaces not done earlier. We also study some basic properties of strong A-statistical…
The aim of this paper is to establish a strong convergence theorem for a strongly nonexpansive sequence in a Banach space. We also deal with some applications of the convergence theorem.
We study some properties convex functions fulfill. Among the conclusions we obtain from such result, we are able to prove some nontrivial inequalities among real numbers, and we give an improvement of the reverse triangle inequality in the…