Deferred 𝜎-statistical summability in intuitionistic fuzzy 𝑟-normed linear spaces

Abstract

In this paper, we define and study three novel summability concepts – strong deferred 𝜎-summability, deferred 𝜎-statistical summability, and 𝜎-statistical summability in intuitionistic fuzzy 𝑟-normed linear spaces (briefly called IF-𝑟-NLS) by using 𝜎-mean. We also provide an example in support of the new notions and uncover some interesting relationships. Additionally, we study deferred 𝜎-statistical summability in the context of two pairs of sequences of positive integers, namely, α n , γ n \alpha_{n},\gamma_{n} , and u n , v n u_{n},v_{n} satisfying α n ≤ u n < v n ≤ γ n \alpha_{n}\leq u_{n} .