On the Zweier Sequence Spaces of Fuzzy Numbers

Abstract

It was given a prototype constructing a new sequence space of fuzzy numbers by means of the matrix domain of a particular limitation method. That is we have constructed the Zweier sequence spaces of fuzzy numbers [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη consisting of all sequences u=(uk) such that Zηu in the spaces ℓ∞(F), c(F), and c0(F), respectively. Also, we prove that [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη are linearly isomorphic to the spaces ℓ∞(F), c(F), and c0(F), respectively. Additionally, the α(r)-, β(r)-, and γ(r)-duals of the spaces [ℓ∞(F)]Zη, [c(F)]Zη, and [c0(F)]Zη have been computed. Furthermore, two theorems concerning matrix map have been given.