Research ArticleOpen AccessGoogle Scholar indexed
On Some <i>I</i>-Convergent Double Sequence Spaces Defined by a Modulus Function
Department of Mathematics, Aligarh Muslim University, Aligarh, India
Department of Mathematics, Aligarh Muslim University, Aligarh, India
- 1 Department of Mathematics, Aligarh Muslim University, Aligarh, India
- 2 Department of Mathematics, Aligarh Muslim University, Aligarh, India
Copy link · social · email
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.
KeywordsIdealFilterModulus FunctionLipschitz FunctionI-Convergence FieldI-ConvergentMonotone and Solid Double Sequence Spaces
- H. Fast, “Sur la Convergence Statistique,” Colloqium Mathematicum, Vol. 2, No. 1, 1951, pp. 241-244.
- J. A. Fridy, “On Statistical Convergence,” Analysis, Vol. 5, 1985, pp. 301-313.
- J. A. Fridy, “Statistical Limit Points,” Proceedings of American Mathematical Society, Vol. 11, 1993, pp. 11871192. doi:10.1090/S0002-9939-1993-1181163-6
- P. Kostyrko, T. Salat and W. Wilczynski, “I-Convergence,” Real Analysis Exchange, Vol. 26, No. 2, 1999, pp. 193-200.
- T. Salat, B. C. Tripathy and M. Ziman, “On Some Properties of I-Convergence,” Tatra Mountain Mathematical Publications, 2000, pp. 669-686.
- K. Demirci, “I-Limit Superior and Limit Inferior,” Mathematical Communications, Vol. 6, 2001, pp. 165-172.
- T. J. I. Bromwich, “An Introduction to the Theory of Infinite Series,” MacMillan Co. Ltd., New York, 1965.
- M. Basarir and O. Solancan, “On Some Double Sequence Spaces,” Journal of the Indian Academy of Mathematics, Vol. 21, No. 2, 1999, pp. 193-200.
- H. Nakano, “Concave Modulars,” Journal of Mathematical Society, Japan, Vol. 5, No. 1, 1953, pp. 29-49. doi:10.2969/jmsj/00510029
- W. H. Ruckle, “On Perfect Symmetric BK-Spaces,” Mathematische Annalen, Vol. 175, No. 2, 1968, pp. 121-126. doi:10.1007/BF01418767
- W. H. Ruckle, “FK-Spaces in Which the Sequence of Coordinate Vectors is Bounded,” Canadian Journal of Mathematics, Vol. 25, No. 5, 1973, pp. 973-975. doi:10.4153/CJM-1973-102-9
- B. Gramsch, “Die Klasse Metrisher Linearer Raume L(φ),” Mathematische Annalen, Vol. 171, 1967, pp. 6178. doi:10.1007/BF01433094
- D. J. H. Garling, “On Symmetric Sequence Spaces,” Proceedings of London Mathematical Society, Vol. 16, 1966, pp. 85-106. doi:10.1112/plms/s3-16.1.85
- D. J. H. Garling, “Symmetric Bases of Locally Convex Spaces,” Studia Mathematica, Vol. 30, No. 2, 1968, pp. 163-181.
- G. Kothe, “Topological Vector Spaces,” Springer, Berlin, 1970.
- W. H. Ruckle, “Symmetric Coordinate Spaces and Symmetric Bases,” Canadian Journal of Mathematics, Vol. 19, 1967, pp. 828-838. doi:10.4153/CJM-1967-077-9
- V. A. Khan and S. Tabassum, “On Some New Double Sequence Spaces of Invariant Means Defined by Orlicz Function,” Communications, Faculty of Sciences, University of Ankara, Vol. 60, 2011, pp. 11-21.