On paranorm BVσ I-convergent double sequence spaces defined by an Orlicz function

Vakeel A. Khan; Hira Fatima; Sameera A. A. Abdullah; Kamal M. A. S. Alshlool

doi:10.1515/anly-2017-0004

Article

On paranorm BV_σ I-convergent double sequence spaces defined by an Orlicz function

Vakeel A. Khan , Hira Fatima , Sameera A. A. Abdullah and Kamal M. A. S. Alshlool

Published/Copyright: July 28, 2017

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From the journal Analysis Volume 37 Issue 3

Abstract

The space BVσ was introduced and studied by Mursaleen [21]. In the present article we study the double sequence spaces (0BV(M,p)σI)2, BV2(M,p)σI and (∞BV(M,p)σI)2 with the help of the space BVσ and an Orlicz function M, where p=(pi⁢j) is the double sequence of strictly positive real numbers. We study some of its properties and prove some inclusion relations related to these new spaces.

Keywords: Bounded variation; invariant mean; ideal; filter; Orlicz function,I-convergence; I-null; solid space; sequence algebra; convergence free space; paranorm

MSC 2010: 40C05; 46A45; 46E30; 46E40; 46B20

Acknowledgements

The authors would like to record their gratitude to the reviewer for his careful reading, and for making some useful corrections which improved the presentation of the paper.

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Received: 2017-2-1

Revised: 2017-6-7

Accepted: 2017-6-15

Published Online: 2017-7-28

Published in Print: 2017-8-1

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Articles in the same Issue

https://doi.org/10.1515/anly-2017-0004

Keywords for this article

Bounded variation; invariant mean; ideal; filter; Orlicz function,I-convergence; I-null; solid space; sequence algebra; convergence free space; paranorm