Related papers: Some remarks on almost locally uniformly rotund po…

In this paper, we deal with uniform spaces whose diagonal uniformity admits a basis consisting of equivalence relations. Such non-Archimedean uniform spaces are particularly interesting for applications in commutative ring theory, because…

These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach…

This paper presents new approaches to the fixed point property for nonexpansive mappings in L^1 spaces. While it is well-known that L^1 fails the fixed point property in general, we provide a complete and self-contained proof that…

In this paper, we extend the Banach contraction principle to metric-like as well as partial metric spaces (not essentially complete) equipped with an arbitrary binary relation. Thereafter, we derive some fixed point results which are…

In this paper, we consider abstract nonautonomous difference inclusions in locally convex spaces with integer order differences. We particularly analyze the existence and uniqueness of almost periodic type solutions to abstract…

Angular equivalence is introduced and shown to be an equivalence relation among the norms on a fixed real vector space. It is a finer notion than the usual (topological) notion of norm equivalence. Angularly equivalent norms share certain…

We extend the result of B. Cascales at al. about expand-contract plasticity of the unit ball of strictly convex Banach space to those spaces whose unit ball is the union of all its finite-dimensional polyhedral extreme subsets. We also…

Another proof that uniformly nonsquare Banach spaces have the fixed point property is presented.

We show that the classes of separable reflexive Banach spaces and of spaces with separable dual are strongly bounded. This gives a new proof of a recent result of E. Odell and Th. Schlumprecht, asserting that there exists a separable…

Given $A$ and $B$ two nonempty subsets in a metric space, a mapping $T : A \cup B \rightarrow A \cup B$ is relatively nonexpansive if $d(Tx,Ty) \leq d(x,y) \text{for every} x\in A, y\in B.$ A best proximity point for such a mapping is a…

We develop tools to produce equivalent norms with specific local geometry around infinitely many points in the sphere of a Banach space via an inductive procedure. We combine this process with smoothness results and techniques to solve two…

We prove that the class of reflexive asymptotic-$c_0$ Banach spaces is coarsely rigid, meaning that if a Banach space $X$ coarsely embeds into a reflexive asymptotic-$c_0$ space $Y$, then $X$ is also reflexive and asymptotic-$c_0$. In order…

We introduce and study two new relations between function spaces over measure spaces of infinite measure, motivated by the question of establishing compactness. The first relation captures the uniform decay of function (quasi-)norms ``at…

New concepts related to approximating a Lipschitz function between Banach spaces by affine functions are introduced. Results which clarify when such approximations are possible are proved and in some cases a complete characterization of the…

We show that every metric space with bounded geometry uniformly embeds into an explicit reflexive Banach space (a direct sum of l^p spaces). In the case of discrete groups we show the analogue of a-T-menability. That is, we construct a…

The purpose of this paper is to study an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth and uniformly convex Banach space with respect to a left regular sequence of means defined on an…

We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a…

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the…

We define the notion of isometric envelope of a subspace in a Banach space, and relate it to a) the mean ergodic projection on the space of fixed points of a semigroup of contractions, b) results on Korovkin sets from the 70's, and c)…

The duality of uniform approximation property for Banach spaces is well known. In this note, we establish, under the assumption of local reflexivity, the duality of uniform approximation property in the category of operator spaces.