REITERATIVE (m_{n})-DISTRIBUTIONAL CHAOS FOR BINARY RELATIONS OVER METRIC SPACES

Abstract

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