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

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, <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>α</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>γ</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:math> αₙ,γₙ , and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>u</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mi>v</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:math> uₙ,vₙ satisfying <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>α</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>≤</m:mo> <m:msub> <m:mi>u</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo><</m:mo> <m:msub> <m:mi>v</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>≤</m:mo> <m:msub> <m:mi>γ</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:math> αₙ≤ uₙ<vₙ≤γₙ .