This study defines f-devaney chaos and examines its properties in infinite metric spaces, suggesting implications for f-sensitivity.
We define and study stronger forms of Devaney chaos and name it as F-Devaney chaos, where F is a family of subsets of N. Examples of maps which is Fₜ-Devaney chaotic but not Fcf-Devaney chaotic, Fₛ-Devaney chaotic but neither Fₜ-Devaney chaotic nor Fcf-Devaney chaotic are discussed. Further, we show that for the maps on infinite metric space without isolated points, F-sensitivity is a redundant condition in the definition F-Devaney chaos. Here F=Fₛ, \: Fₜ, \: Fₜₛ or Fcf. We also obtain conditions under which Devaney chaos implies Fₛ-Devaney chaos or Fₜ-Devaney chaos. Next, we define the concept of (F, G)-P-chaos and obtain conditions under which (F₁, G₁)-P-chaos implies F-Devaney chaos for different families F₁ and G₁.
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Joshi et al. (2025) studied this question.
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