Banach Spaces and Fixed-Point Theorems

  • Eberhard Zeidler
Part of the Applied Mathematical Sciences book series (AMS, volume 108)

Abstract

In a Banach space, the so-called norm
$$ \parallel u\parallel = nonnegativenumber \hfill \\ $$
is assigned to each element u. This generalizes the absolute value |u of a real number u. The norm can be used in order to define the convergence
$$ \mathop {\lim }\limits_{n \to \infty } {u_n} = u \hfill \\ $$
by means of
$$ \mathop {\lim }\limits_{n \to \infty } \parallel {u_n} - u\parallel = 0. \hfill \\ \parallel u\parallel = nonnegativenumber \hfill \\ $$

Keywords

Hull Dition Verse Summing 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Eberhard Zeidler
    • 1
  1. 1.Max-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

Personalised recommendations