Reiterative (m_n)-distributional chaos for binary relations over metric spaces

Abstract

The paper intends to be a heuristical study. Let $(m_n)$ be an increasing sequence in $[1,\infty)$ satisfying $\lim_{n\rightarrow\infty}\frac{m_n}{n}$, $\lambda\in(0,1]$, $s\in\{0,1-,1+,2-\}$ and $i\in{\mathbb N}\cap[1,20]$. we introduce and analyze the concepts of reiterative $(m_n,\tilde{X})$-distributional chaos of type s, reiterative $(\lambda, \tilde{X})$-distributional chaos of type s, reiterative $[\tilde{X},m_n,i]$-distributional chaos and reiterative $[\tilde{X},\lambda,i]$-distributional chaos for general sequences of binary relations over metric spaces.