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Reiterative \(m_{n}\)-Distributional Chaos of Type s in Fréchet Spaces

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Abstract

The main aim of this paper is to consider various notions of (dense) \(m_{n}\)-distributional chaos of type s and (dense) reiterative \(m_{n}\)-distributional chaos of type s for general sequences of linear not necessarily continuous operators in Fréchet spaces. Here, \((m_{n})\) is an increasing sequence in \([1,\infty )\) satisfying \(\liminf _{n\rightarrow \infty }\frac{m_{n}}{n}>0\) and s could be \(0,1,2,2+,2\frac{1}{2},3,1+,2-,2_{Bd},2_{Bd}+\). We investigate \(m_{n}\)-distributionally chaotic properties and reiteratively \(m_{n}\)-distributionally chaotic properties of some special classes of operators like weighted forward shift operators and weighted backward shift operators in Fréchet sequence spaces, considering also continuous analogues of introduced notions and some applications to abstract partial differential equations.

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Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, 21125, Serbia

    Marko Kostić

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  1. Marko Kostić
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Correspondence to Marko Kostić.

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Communicated by Mohammad Sal Moslehian.

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The author is partially supported by Grant 174024 of Ministry of Science and Technological Development, Republic of Serbia.

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Kostić, M. Reiterative \(m_{n}\)-Distributional Chaos of Type s in Fréchet Spaces. Bull. Malays. Math. Sci. Soc. 43, 3963–4005 (2020). https://doi.org/10.1007/s40840-020-00906-x

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  • DOI: https://doi.org/10.1007/s40840-020-00906-x

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