Normed uniformly reflexive structures

NORMED UNIFORMLY REFLEXIVE STRUCTURES Henk Barendregt Mathematisch Instituut

Uniformly convex Banach spaces are reflexive - constructively

We propose a natural definition of what it means in a constructive context for a Banach space to be reflexive, and then prove a constructive counterpart of the MilmanPettis theorem that uniformly convex Banach spaces are reflexive. Our aim in this note is to present a fully constructive analysis of the Milman-Pettis theorem [11, 12, 9, 13]: a uniformly convex Banach space is reflexive. First, t...

The Ribe Programme

In 1976 Ribe [R] proved that uniformly homeomorphic Banach spaces have uniformly linearly isomorphic finite-dimensional subspaces: that if there is a uniformly continuous homeomorphism between two Banach spaces, with uniformly continuous inverse, then every finite-dimensional subspace of one space, is linearly isomorphic to a subspace of the other, with an implied constant of isomorphism indepe...

Browder’s Fixed Point Theorem and Some Interesting Results in Intuitionistic Fuzzy Normed Spaces

We define and study Browder's fixed point theorem and relation between an intuitionistic fuzzy convex normed space and a strong intuitionistic fuzzy uniformly convex normed space. Also, we give an example to show that uniformly convex normed space does not imply strongly intuitionistic fuzzy uniformly convex.

Existence Results of best Proximity Pairs for a Certain Class of Noncyclic Mappings in Nonreflexive Banach Spaces Polynomials 

Introduction Let  be a nonempty subset of a normed linear space . A self-mapping  is said to be nonexpansive provided that  for all . In 1965, Browder showed that every nonexpansive self-mapping defined on a nonempty, bounded, closed and convex subset of a uniformly convex Banach space , has a fixed point. In the same year, Kirk generalized this existence result by using a geometric notion of ...