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A fixed point theorem and equilibrium point of an abstract economy

✍ Scribed by E. Tarafdar


Book ID
107949681
Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
457 KB
Volume
20
Category
Article
ISSN
0304-4068

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A fixed-point theorem of Krasnoselskii
✍ T.A Burton πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 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