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A fixed-point theorem of Krasnoselskii

✍ Scribed by T.A Burton

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
193 KB
Volume
11
Category
Article
ISSN
0893-9659

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✦ Synopsis

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 = Bx + Ay. The proof also yields a technique for showing that such x is in M.

📜 SIMILAR VOLUMES

A Fixed Point Theorem of Krasnoselskii—S
A Fixed Point Theorem of Krasnoselskii—Schaefer Type
✍ T. A. Burton; Colleen Kirk 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 351 KB

In this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a Tperiodic solution of z(t) = a(t) + D(t, s)g(s, z(s)) ds 6, if D and g satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping t