On Some I-Convergent Double Sequence Spaces Defined by a Modulus Function - Engineering

ENG > Vol.5 No.5, May 2013

On Some I-Convergent Double Sequence Spaces Defined by a Modulus Function ()

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DOI: 10.4236/eng.2013.55A006 5,468 Downloads 7,571 Views Citations

Author(s)

Vakeel. A. Khan, Nazneen Khan

Affiliation(s)

Department of Mathematics, Aligarh Muslim University, Aligarh, India.

ABSTRACT

In 2000, Kostyrko, Salat, and Wilczynski introduced and studied the concept of I-convergence of sequences in metric spaces where I is an ideal. The concept of I-convergence has a wide application in the field of Number Theory, trigonometric series, summability theory, probability theory, optimization and approximation theory. In this article we introduce the double sequence spaces

and

,for a modulus function f and study some of the properties of these spaces.

KEYWORDS

Ideal; Filter; Modulus Function; Lipschitz Function; I-Convergence Field; I-Convergent; Monotone and Solid Double Sequence Spaces

Share and Cite:

V. Khan and N. Khan, "On Some I-Convergent Double Sequence Spaces Defined by a Modulus Function," Engineering, Vol. 5 No. 5A, 2013, pp. 35-40. doi: 10.4236/eng.2013.55A006.

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