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On some results related to the Karlsson-Nussbaum conjecture in geodesic spaces

Aleksandra Huczek

Abstract

We show a Wolff-Denjoy type theorem in the case of a one-parameter continuous semigroups of nonexpansive mappings in which there is a compact mapping. Using the notion of attractor we are also able to prove some specific properties directly related to the Karlsson-Nussbaum conjecture.

On some results related to the Karlsson-Nussbaum conjecture in geodesic spaces

Abstract

We show a Wolff-Denjoy type theorem in the case of a one-parameter continuous semigroups of nonexpansive mappings in which there is a compact mapping. Using the notion of attractor we are also able to prove some specific properties directly related to the Karlsson-Nussbaum conjecture.
Paper Structure (5 sections, 24 theorems, 94 equations)

This paper contains 5 sections, 24 theorems, 94 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Wolff-Denjoy theorems for semigroups
  4. Attractor of a nonexpansive mapping
  5. Attractor of a semigroup of nonexpansive mappings

Key Result

Lemma 2.1

Let $(Y,d)$ satisfy Axiom $3'$, $z_{0}\in Y$, $\zeta \in \partial Y$ and $r\in \mathbb{R}$. Then

Theorems & Definitions (34)

  • Lemma 2.1
  • Theorem 2.2
  • proof
  • Theorem 2.3
  • Theorem 3.1
  • Lemma 3.2
  • Theorem 3.3
  • Theorem 3.4
  • proof
  • Corollary 3.5
  • ...and 24 more