<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the inductive mean, which extends the von Neumann linear ergodic theorem. The main result shows that the sequence given by the inductive means of iterations of an affine nonexpansive mapping with a nonempty fixed point set converges strongly to a fixed point of the mapping. A Tauberian theorem is also proved in order to ensure convergence of the iterations.</p></abstract>

In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the inductive mean, which extends the von Neumann linear ergodic theorem. The main result shows that the sequence given by the inductive means of iterations of an affine nonexpansive mapping with a nonempty fixed point set converges strongly to a fixed point of the mapping. A Tauberian theorem is also proved in order to ensure convergence of the iterations.

A Mean Ergodic Theorem for Affine Nonexpansive Mappings in Nonpositive Curvature Metric Spaces

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

In this paper, we consider the orbits of an affine nonexpansive mapping in Hadamard (nonpositive curvature metric) spaces and prove an ergodic theorem for the...

A Mean Ergodic Theorem for Affine Nonexpansive Mappings in Nonpositive Curvature Metric Spaces

Publié en ligne: 13 avr. 2021

Pages: 111 - 125

Reçu: 01 avr. 2020

Accepté: 04 mai 2020

DOI: https://doi.org/10.2478/auom-2021-0008

Mots clés
Ergodic Theorem, Hadamard Space, Inductive Mean, Affine Nonexpansive Mapping, Tauberian Condition

© 2021 Hadi Khatibzadeh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

A Mean Ergodic Theorem for Affine Nonexpansive Mappings in Nonpositive Curvature Metric Spaces

Publié en ligne: 13 avr. 2021

Pages: 111 - 125

Reçu: 01 avr. 2020

Accepté: 04 mai 2020

DOI: https://doi.org/10.2478/auom-2021-0008

Mots clésErgodic Theorem, Hadamard Space, Inductive Mean, Affine Nonexpansive Mapping, Tauberian Condition

© 2021 Hadi Khatibzadeh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
Ergodic Theorem, Hadamard Space, Inductive Mean, Affine Nonexpansive Mapping, Tauberian Condition