Related papers: Uniformly convex-transitive function spaces
We investigate the connections between UC and UC* properties for ordered pairs of subsets (A,B) in metric spaces, which are involved in the study of existence and uniqueness of best proximity points. We show that the $UC^{*}$ property is…
Non-convex functions that yet satisfy a condition of uniform convexity for non-close points can arise in discrete constructions. We prove that this sort of discrete uniform convexity is inherited by the convex envelope, which is the key to…
We construct a Banach space satisfying that the nearest point map (also called proximity mapping or metric projection) onto any compact and convex subset is continuous but not uniformly continuous. The space we construct is locally…
It is known that a Banach space contains an isomorphic copy of $c_0$ if, and only if, it can be equivalently renormed to be almost square. We introduce and study transfinite versions of almost square Banach spaces with the purpose to relate…
In this survey, we discuss the definition of a (quasi-)Banach function space. We advertise the original definition by Zaanen and Luxemburg, which does not have various issues introduced by other, subsequent definitions. Moreover, we prove…
Another proof that uniformly nonsquare Banach spaces have the fixed point property is presented.
We prove that a Banach space has the uniform approximation property with proportional growth of the uniformity function iff it is a weak Hilbert space.
We present a generalization of the Radon-Riesz property to sequences of continuous functions with values in uniformly convex and uniformly smooth Banach spaces.
This is the first of two closely related papers on transversality. Here we introduce the notion of tangential transversality of two closed subsets of a Banach space. It is an intermediate property between transversality and…
We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
We characterise the class of those Banach spaces in which every convex combination of slices of the unit ball intersects the unit sphere as the class of those spaces in which every convex combination of slices of the unit ball contains two…
In this paper we first take a detail survey of the study of the Banach-Saks property of Banach spaces and then show the Banach-Saks property of the product spaces generated by a finite number of Banach spaces having the Banach-Saks…
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We…
In this paper we defined some function spaces on time scale which are Banach spaces respect to supremum norm. We study integral transformations which are carry to some important properties between mentioned above function spaces.
We introduce and study the topological concepts of chain transitivity, mixing and chain mixing property for dynamical systems induced by uniform hyperspaces. These notions generalize the relevant concepts for metric spaces.
We introduce notions of concavity for functions on balanced polyhedral spaces, and we show that concave functions on such spaces satisfy several strong continuity properties.
We study dentable maps from a closed convex subset of a Banach space into a metric space as an attempt of generalize the Radon-Nikod\'ym property to a "less linear" frame. We note that a certain part of the theory can be developed in rather…
In this paper we explore some basic properties of quasi-Banach function spaces which are important in applications. Namely, we show that they posses a generalised version of Riesz--Fischer property, that embeddings between them are always…
In functional analysis it is of interest to study the following general question: Is the uniform version of a property that holds in all Banach spaces also valid in all Banach spaces? Examples of affirmative answers to the above question…