Double Sequence Space of Fuzzy Real Numbers Defined by Orlicz Function

Abstract

The theory of fuzzy logic and the fuzzy set has been successfully applied in various fields of research in social science, management science, and mathematics. In this paper, we use the concept of Fuzzy real numbers to introduce and study the new double sequence spaces l∞ (M, λ, ρ), C F (M, λ, ρ) and CoF (M, λ, ρ) of fuzzy real numbers defined by the Orlicz function and study some of their properties like linear space structure, completeness, and solidness.

On Topological Structure of Total Paranormed Double Sequence Space (ℓ 2 ((X, ||.||), γ, ¯ w¯), G)

“…The concept of paranorm is closely related to the linear metric space; see Wilansky [26] and its studies on sequence spaces were initiated by Maddox [9], and many others. Basarir and Altundag [1], Ghimire, & Pahari [2,3], Parasar and Choudhary [15], Paudel and Pahari [18,20,21] and many others further studied the various types of paranormed sequence spaces.…”

“…They also studied the various types of topological structures of vector valued sequence spaces defined by Orlicz function endowed with suitable natural paranorms and extended some of them in 2-normed spaces. Recently, Paudel, Pahari and et al [17,18,19,20,21,22] has extended the the concepts of sequence space of complex numbers to the sequences of fuzzy real numbers.…”

SOME SUMMABILITY TECHNIQUES IN INFINITE SERIES & SEQUENCE

“…It attempts to create an algorithm that assigns a limit to non-convergent sequences; The theory makes a non-convergent series converge, in a general sense, whenever a sequence of positive linear operators doesn't ordinarily converge. Several workers like Ghimire and Pahari ([5] , [6]) Pahari,Pahari ([11], [12]), Paudel, Pahari,and Kumar ( [13], [14]), etc. have made their contribution and enriched the theory in sequences.…”