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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

Banach Space Linear Space Normed Space Banach Algebra Cauchy Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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

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