Fixed set theorems of Krasnoselskii type

Ok, Efe

doi:10.1090/S0002-9939-08-09332-5

Fixed set theorems of Krasnoselskii type
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by Efe A. Ok PDF

Proc. Amer. Math. Soc. 137 (2009), 511-518 Request permission

Abstract:

We revisit the fixed point problem for the sum of a compact operator and a continuous function, where the domain on which these maps are defined is not necessarily convex, the former map is allowed to be multi-valued, and the latter to be a semicontraction and/or a suitable nonexpansive map. In this setup, guaranteeing the existence of fixed points is impossible, but two types of invariant-like sets are found to exist.

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