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Fixed point theorems for discontinuous functions and applications

โœ Scribed by Ludwig J. Cromme

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
388 KB
Volume
30
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

Fixed points, almost fixed points, discontinuous functions,measure of discontinuity, set-valued functions, integer labeling, vector labeling, mean-value-theorem, neural nets, exchange economy.

1. FIXED POINT THEOREMS

Brouwer's famous fixed point theorem captivates by it's simplicity, depth, and applicability.

THEOREM l [Fixed point theorem, Brouwer, 1912]. With X C R ~ compact 1 and convex, f : X -~ X a continuous mapping there exists a fixed point off:

3x" ~x:f(x')=

x'.

๐Ÿ“œ SIMILAR VOLUMES

A fixed point theorem for discontinuous
A fixed point theorem for discontinuous functions
โœ P. Jean-Jacques Herings; Gerard van der Laan; Dolf Talman; Zaifu Yang ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 153 KB

Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

Fixed-point theorems for discontinuous m
Fixed-point theorems for discontinuous multivalued operators on ordered spaces with applications
โœ B.C. Dhage ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 871 KB

A b s t r a c t --I n this paper, some fixed-point theorems for discontinuous multivalued operators on ordered spaces are proved. These theorems improve the earlier known fixed-point theorems of [1,2]. The main fixed-point theorems are applied to first-order discontinuous differential inclusions for