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Krasnoselskii's fixed point theorem and stability

โœ Scribed by T.A. Burton; Tetsuo Furumochi


Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
92 KB
Volume
49
Category
Article
ISSN
0362-546X

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A fixed-point theorem of Krasnoselskii
โœ T.A Burton ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 193 KB

Krasnoselskii's fixed-point theorem asks for a convex set M and a mapping Pz = Bz + Az such that: (i) Bx+AyEM for eachx, yE M, (ii) A is continuous and compact, (iii) B is a contraction. Then P has a fixed point. A careful reading of the proof reveals that (i) need only ask that Bx + Ay E M when x