Fixed set theorems of krasnoselskiǐ type

Efe A. Ok

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

Fixed set theorems of krasnoselskiǐ type

Efe A. Ok

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	511-518
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-08-09332-5
State	Published - Feb 2009

Keywords

Fixed sets
Krasnoselskiǐ fixed point theorem
Nonexpansive maps

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-08-09332-5

Cite this

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AB - 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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KW - Krasnoselskiǐ fixed point theorem

KW - Nonexpansive maps

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Fixed set theorems of krasnoselskiǐ type

Abstract

Keywords

ASJC Scopus subject areas

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