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Remark on Krasnoselskii’s fixed point theorem

✍ Scribed by Cristian Vladimirescu


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
326 KB
Volume
71
Category
Article
ISSN
0362-546X

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A fixed-point theorem of Krasnoselskii
✍ T.A Burton 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 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