On ideal convergent interval valued generalized difference classes defined by Orlicz function

Abstract

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. A sequence (x_k) of real numbers is said to be I - convergent to a real number ℓ, if for each ε>0 the set {k : |x_k - ℓ|≥ε} belongs to I . In this paper, using ideal convergence, the difference operator Δ^m and Orlicz functions, we introduce and examine some generalized difference sequences of interval numbers. We prove completeness properties of these spaces. Further, we investigate some inclusion relations related to these spaces.

Keywords:

• Sequence space
• Interval numbers
• Difference sequence
• Completeness

2000 Mathematics Subject Classification:

• Primary 40A05
• Secondary 46A70
• 40A99
• 46A99