### 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 | |

State | Published - Feb 2009 |

### Fingerprint

### Keywords

- Fixed sets
- Krasnoselskiǐ fixed point theorem
- Nonexpansive maps

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*137*(2), 511-518. https://doi.org/10.1090/S0002-9939-08-09332-5

**Fixed set theorems of krasnoselskiǐ type.** / Ok, Ahmet.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 2, pp. 511-518. https://doi.org/10.1090/S0002-9939-08-09332-5

}

TY - JOUR

T1 - Fixed set theorems of krasnoselskiǐ type

AU - Ok, Ahmet

PY - 2009/2

Y1 - 2009/2

N2 - 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.

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.

KW - Fixed sets

KW - Krasnoselskiǐ fixed point theorem

KW - Nonexpansive maps

UR - http://www.scopus.com/inward/record.url?scp=77950534026&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950534026&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09332-5

DO - 10.1090/S0002-9939-08-09332-5

M3 - Article

AN - SCOPUS:77950534026

VL - 137

SP - 511

EP - 518

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -