New type of Lacunary Orlicz Difference Sequence Spaces Generated By Infinite Matrices

The main purpose of this paper is to introduce the spaces w ^ θ o [ A , M , Δ , p ] , w ^ θ [ A , M , Δ , p ] and w ^ θ ∞ [ A , M , Δ , p ] generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of S ^ θ [ A , Δ ] –sta...

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Bibliographic Details
Published in:Filomat 2016-01, Vol.30 (12), p.3195-3208
Main Authors: Esi, Ayhan, Bipan, Hazarika, Esi, Ayten
Format: Article
Language:English
Subjects:
Abstract spaces
Banach space
College mathematics
Mathematical sequences
Matrices
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Summary:The main purpose of this paper is to introduce the spaces w ^ θ o [ A , M , Δ , p ] , w ^ θ [ A , M , Δ , p ] and w ^ θ ∞ [ A , M , Δ , p ] generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of S ^ θ [ A , Δ ] –statistical convergence and derive some results between the spaces S ^ θ [ A , Δ ] and w ^ θ [ A , Δ ] . Further, we study some geometrical properties such as order continuous, the Fatou property and the Banach-Saks property of the new space w ^ θ a ∞ [ A , Δ , p ] . Finally, we introduce the notion of S ^ θ [ A , Δ ] –statistical convergence of order α of real number sequences and obtain some inclusion relations between the set of S ^ [ A , Δ ] –statistical convergence of order α.
ISSN:0354-5180
2406-0933
DOI:10.2298/FIL1612195E