Fixed points of endomorphisms of certain free products

Fixed Points of Endomorphisms of a Free Metabelian Group

We consider IA-endomorphisms (i.e. Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the well-known characterization of eigenvectors of a linear operator in a vector space. We then use our matrix characterization to elaborate several properties of the fixed point groups of met...

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

The Universal Functorial Equivariant Lefschetz Invariant

We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K0 of the category of “φ-endomorphisms of finitely generated free RΠ(G,X)-modules”. We derive results about fixed points of equivariant endomorphisms of cocompact proper smooth G-manifolds.

EXISTENCE OF FIXED POINTS OF CERTAIN CLASSES OF NONLINEAR MAPPINGS

In this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $Phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. The results generalise the results of several authors in literature including Xiang [Chang He Xiang, Fixed point theorem for generalized $Phi$-pseudocontra...

Fixed points of endomorphisms of graph groups

It is shown, for a given graph group G, that the fixed point subgroup Fix' is finitely generated for every endomorphism ' of G if and only if G is a free product of free abelian groups. The same conditions hold for the subgroup of periodic points. Similar results are obtained for automorphisms if the dependence graph of G is a transitive forest.