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Journal of Applied Sciences
  Year: 2017 | Volume: 17 | Issue: 9 | Page No.: 467-474
DOI: 10.3923/jas.2017.467.474
 
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Some New Spaces of Ideal Convergent Double Sequences by Using Compact Operator

Vakeel Ahmad Khan , Rami K.A. Rababah, Ayhan Esi , Sameera Ameen Ali Abdullah and Kamal Mohammed Ali Suleiman Alshlool

Abstract:
Background and Objective: This study comes from the notion of I-convergence which is the generalization of statistical convergence. The idea of I-convergent sequence spaces was motivated by the statistical convergence for double sequence. The I-convergence for double sequence in real line and general metric space. Methodology: This has motivated us to study the ideal convergence for double sequences using compact operator and define these spaces , and . Further, inclusion relations between these spaces and some properties such as solidity and monotonic was investigated. Results: This study consists of two sections. In the first section, it was given the basic definitions related to double sequences, compact operator, ideal, filter etc. The second section deals with the main results like , and are linear spaces and normed spaces. It was defined a real valued function on as h(x) = I-lim x and proved that this function is Lipschitz continuous and hence uniformly continuous. At the last, topological properties of these spaces like monotonicity and solidity are discussed. Conclusion: This study has used compact linear operator to define spaces of ideal convergent double sequence , and which provide better tool to study a more general spaces of sequences.
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How to cite this article:

Vakeel Ahmad Khan, Rami K.A. Rababah, Ayhan Esi, Sameera Ameen Ali Abdullah and Kamal Mohammed Ali Suleiman Alshlool, 2017. Some New Spaces of Ideal Convergent Double Sequences by Using Compact Operator. Journal of Applied Sciences, 17: 467-474.

DOI: 10.3923/jas.2017.467.474

URL: https://scialert.net/abstract/?doi=jas.2017.467.474

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