On the Interrelationship Between Various Forms of (F, G)-Shadowing Property

The aim of this paper is to study the interrelationship between various forms of ( F , G )-shadowing property and represent it through the diagram. We show that asymptotic shadowing is equivalent to (ℕ 0 , F 𝑐𝑓 )-shadowing property and that (ℕ 0 , F 𝑐𝑓 )-shadowing implies ( F 𝑐𝑓 , F 𝑐𝑓 )-shadowing. Necessary examples are discussed to support the diagram. We also give characterization for maps to have the ( F , G )-shadowing property through the shift map on the inverse limit space. Further, we relate the ( F , G )-shadowing property to the positively F 𝑠 -expansive map. Also, we obtain the necessary and sufficient condition for the identity map to have (ℕ 0 , F 𝑡 )-shadowing property.