Z2k-actions with a special fixed point set

A fixed point result for a new class of set-valued contractions

In this paper, we introduce a new class of set-valued contractions and obtain a xed point theoremfor such mappings in complete metric spaces. Our main result generalizes and improves many well-known xed point theorems in the literature.

Structure of the Fixed Point of Condensing Set-Valued Maps

In this paper, we present structure of the fixed point set results for condensing set-valued map. Also, we prove a generalization of the Krasnosel'skii-Perov connectedness principle to the case of condensing set-valued maps.

Fixed Point Formulas and Loop Group Actions

In this paper we present a new fixed point formula associated with loop group actions on infinite dimensional manifolds. This formula provides information for certain infinite dimensional situations similarly as the well known Atiyah-BottSegal-Singer’s formula does in finite dimension. A generalization of the latter to orbifolds will be used as an intermediate step. There exist extensive litera...

Most Homeomorphisms with a Fixed Point Have a Cantor Set of Fixed Points.

We show that, for any n ≠ 2, most orientation preserving homeomorphisms of the sphere S2n have a Cantor set of fixed points. In other words, the set of such homeomorphisms that do not have a Cantor set of fixed points is of the first Baire category within the set of all homeomorphisms. Similarly, most orientation reversing homeomorphisms of the sphere S2n+1 have a Cantor set of fixed points for...

Fixed Point Theorems for Set-valued Mappings