Uniform Homeomorphisms of Banach Spaces and Asymptotic Structure

The James and von Neumann-Jordan type constants and uniform normal structure in Banach spaces

Recently, Takahashi has introduced the James and von Neumann-Jordan type constants. In this paper, we present some sufficient conditions for uniform normal structure and therefore the fixed point property of a Banach space in terms of the James and von Neumann-Jordan type constants and the Ptolemy constant. Our main results of the paper significantly generalize and improve many known results in...

Uniform Embeddings, Homeomorphisms and Quotient Maps between Banach Spaces (a Short Survey)

Szlenk Indices and Uniform Homeomorphisms

We prove some rather precise renorming theorems for Banach spaces with Szlenk index ω0. We use these theorems to show the invariance of certain quantitative Szlenk-type indices under uniform homeomorphisms.

Uniform Equivalence between Banach Spaces by Israel Aharoni and Joram Lindenstrauss

It is a well-known result of Kadec that every two separable infinite dimensional Banach spaces are homeomorphic. Also in large classes of nonseparable Banach spaces (perhaps all) the density character of a Banach space is its only topological invariant (see the book [2] for details). The situation changes considerably if we consider uniform homeomorphisms. Several results are known which prove ...

Fixed points for E-asymptotic contractions and Boyd-Wong type E-contractions in uniform spaces

In this paper we discuss on the fixed points of asymptotic contractions and Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A new version ofKirk's fixed point theorem is given for asymptotic contractions and Boyd-Wong type contractions is investigated in uniform spaces.