Fixed set theorems of krasnoselskiǐ type

Efe A. Ok

    Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
    Pages (from-to)511-518
    Number of pages8
    JournalProceedings of the American Mathematical Society
    Volume137
    Issue number2
    DOIs
    StatePublished - Feb 2009

    Keywords

    • Fixed sets
    • Krasnoselskiǐ fixed point theorem
    • Nonexpansive maps

    ASJC Scopus subject areas

    • Mathematics(all)
    • Applied Mathematics

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