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A Fixed Point Theorem of Krasnoselskii—Schaefer Type

✍ Scribed by T. A. Burton; Colleen Kirk

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
351 KB
Volume
189
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a Tperiodic solution of z(t) = f(t, 4 t ) ) + D ( t , s)g(., 4 3 ) ) d.9 (0.2) L, if j defines a contraction and if D and g are small enough.

We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when f defines a contraction mapping, while D and g satisfy the aforementioned sign conditions.

1991 Mathematics Subject Classification. Primary: 47H 10, 45M15. Keywords and phrases. Fixed points, integral equations.

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