Related papers: A fixed-point theorem for definably amenable group…

Averaging linear functional on the space continuous functions of the group of diffeomorphisms of interval is found. Amenability of several discrete subgroups of the group of diffeomorphisms $\Diff^3([0,1])$ of interval is prove. In…

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.

Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.

We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows a novel strong convergence phenomenon…

A group is said to be strongly amenable if each of its proximal topological actions has a fixed point. We show that a finitely generated group is strongly amenable if and only if it is virtually nilpotent. More generally, a countable…

We extend Bourgain's return times theorem to arbitrary locally compact second countable amenable groups. The proof is based on a version of the Bourgain--Furstenberg--Katznelson--Ornstein orthogonality criterion.

We prove an analogue of the prime number theorem for finite fields.

Averaging linear functional on the space continuous functions of the group of diffeomorphisms of interval is found. Amenability of several discrete subgroups of the group of diffeomorphisms $\Diff^3([0,1])$ of interval is prove. In…

In this paper, we establish some fixed point theorems in ordered partial metric spaces. An example is given to illustrate our obtained results.

In this paper we generalize Kingman's sub-additive ergodic theorem to a large class of infinite countable discrete amenable group actions.

Gromov showed that for fixed, arbitrarily large C, any uniformly C-Lipschitz affine action of a random group in his graph model on a Hilbert space has a fixed point. We announce a theorem stating that more general affine actions of the same…

A $G$-invariant version of definable Tietze extension theorem for definably complete structures is proved when a definably compact definable topological group $G$ acts definably and continuously on the definable set.

A topological group $G$ is B-amenable if and only if every continuous affine action of $G$ on a bounded convex subset of a locally convex space has an approximate fixed point. Similar results hold more generally for slightly uniformly…

The purpose of this article is prove that Thompson's group F is amenable. The methods developed will then be used to prove a generalization of Hindman's theorem for the free nonassociative binary system on one generator.

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble…

We prove the even isomorphism theorem for Coxeter groups

Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.

The purpose of this article is to present a "Groupoid proof" to the Lefschetz fixed point formula for elliptic complexes. We shall define a "relative version" of tangent groupoid, describe the corresponding pseudodifferential calculi and…

A new fixed point principle for complete ordered families of equivalences (COFEs) is presented, which is stronger than the standard Banach-type fixed point principle.

We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…