International journal of

ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN:2313-626X

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 Volume 6, Issue 9 (September 2019), Pages: 58-63

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 Original Research Paper

 Title: On paranorm I-convergent double sequence spaces defined by a compact operator

 Author(s): Vakeel A. Khan 1, Hira Fatima 1, *, Mohammad Faisal Khan 2, Mohd. Imran Idrisi 1

 Affiliation(s):

 1Department of Mathematics, Aligarh Muslim University, Aligarh, India
 2College of Science and Theoretical Studies, Saudi Electronic University, Riyadh, Saudi Arabia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-4132-0954

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2019.09.009

 Abstract:

In this paper, we extend the concept of ideal convergence of sequences in metric spaces. Recently, the concept of ideal convergent double sequence spaces defined by a compact operator. Motivated by this, we introduce some ideal convergent double sequence spaces with the help of compact operator T on the real space ℝ and a bounded double sequence  of positive real numbers. We examine some basic properties and prove some inclusions relations on these new defined sequence spaces. 

 © 2019 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Compact operator, I-convergence, Sequence algebra, Convergence free space, Paranorm

 Article History: Received 26 February 2019, Received in revised form 5 July 2019, Accepted 7 July 2019

 Acknowledgement:

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

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.

 Citation:

 Khan VA, Fatima H, and Khan MF et al. (2019). On paranorm I-convergent double sequence spaces defined by a compact operator. International Journal of Advanced and Applied Sciences, 6(9): 58-63

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