Deepmala, N. Subramanian, and Lakshmi Narayan Mishra

DOI: 10.14456/sjst-psu.2017.60

pp. 549 - 563

Abstract

Let (A_mn^uv )
A be a sequence of bounded linear operators from a separable Banach metric space of ( X , 0 ) into a Banach
metric space (Y , 0 ).  Suppose that ∅ ∈ Φ is a countable fundamental set of X and the ideal I – of subsets Ν × Ν has property
(AP). The sequence (A_mn^uv )
A is said to b^* I – convergent if it is pointwise I – convergent and there exists an index set K
such that Ν × Ν / K ∈ I and (A_mn^uv )_m,n∈K
 is bounded for any x ∈ X , the concept of lacunary vector valued of _Χ²
 and
the concept of Δ₁₁ –  lacunary statistical convergent vector valued of _Χ²
 of difference sequences have been introduced. In
addition, we introduce interval numbers of asymptotically ideal equivalent sequences of vector valued difference by
Musielak fuzzy real numbers and established some relations related to this concept.
Finally we introduce the notion of interval numbers of Cesáro Orlicz asymptotically equivalent sequences vector
valued difference of Musielak Orlicz function and establish their relationship with other classes