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Research Article | Open Access

Mean chain transitivity and almost mean shadowing property of iterated function systems

Thiyam Thadoi Devi1, Khundrakpam Binod Mangang1( ), Sonika Akoijam1,  Lalhmangaihzuala2, Phinao Ramwungzan3, Jay Prakash Singh4
Department of Mathematics, Manipur University, Canchipur, Imphal, Manipur 795003, India
Department of Mathematics, Government Serchhip College, Serchhip, Mizoram 796181, India
Department of Mathematics, Manipur Technical University, Imphal, Manipur 795004, India
Department of Mathematics, Central University of South Bihar, Gaya, Bihar 824236, India
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Abstract

In this paper, we introduce the notions of mean chain transitivity, mean chain mixing, totally mean chain transitivity, and almost mean shadowing property to iterated function systems (IFS). We study the interrelations of these notions. We prove that an iterated function system is chain transitive if one of the constituent maps is surjective, and it has almost mean shadowing property.

Keywords

transitivityshadowingpseudo-orbitschainsiterated function systems
CLC number: 37B65, 37B99, 26A18

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 20811-20825
DOI: 10.3934/math.20241012

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Cite this article:
Devi TT, Mangang KB, Akoijam S, et al. Mean chain transitivity and almost mean shadowing property of iterated function systems. AIMS Mathematics, 2024, 9(8): 20811-20825. https://doi.org/10.3934/math.20241012

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Received: 03 May 2024
Revised: 18 June 2024
Accepted: 21 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)