Advertisement
Published in:
1995 | OriginalPaper | Chapter
Banach Spaces and Fixed-Point Theorems
Author : Eberhard Zeidler
Published in: Applied Functional Analysis
Publisher: Springer New York
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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 $$ \mathop {\lim }\limits_{n \to \infty } \parallel {u_n} - u\parallel = 0. \hfill \\ \parallel u\parallel = nonnegativenumber \hfill \\ $$