Some topological and algebraic properties of paranorm i-convergent double sequence spaces
Keywords:
Double sequence, ideal, -convergence, paranorm.Abstract
ABSTRACT
In this article some new double sequence spaces , , and for = ( a double sequence of positive real numbers have been introduced. Some algebraic and topological properties of these spaces have been studied. The decomposition theorem and some inclusion relations are proved.
References
REFERENCES
Dems, K. 2004. On I-Cauchy sequences, Real Analysis Exchange 30(1):123-128.
Gökhan, A. & Colak, R. 2004. The double sequence spaces c2(p) and (p), Applied Mathematics & Computations 157(2): 491-501.
Gökhan, A. & Colak, R. 2005. Double sequence space , Applied Mathematics & Computations 160 (1): 147–153.
Gökhan, A. & Colak, R. 2006. On double sequence spaces c2(p) (p) and , International Journal of Pure & Applied Mathematics 30(3): 309-321.
Gürdal, M. 2006. On ideal convergent sequences in 2-normed spaces, Thai Journal Mathematics 4(1): 85-91.
Gürdal, M. & Sahiner, A. 2008. Ideal convergence in n-normal spaces and some new sequence spaces via n-norm, Journal of Fundamental Sciences 4(1): 233-244.
Hazarika, B. 2011. On paranormed ideal convergent generalized difference strongly summable Ssequence spaces defined over n-normed spaces, ISRN Mathematical Analysis 2011 , no 17, doi:10.5402/2011/317423.
Kamthan, P. K. & Gupta, M. 1980. Sequence spaces and series, Marcel Dekker, New York.
Kostyrko, P., Macaj, M., Šalăt, T. & Sleziak, M. 2005. I-convergence and extermal I-limit points, Mathematica Slovaca 55: 443-64.
Kostyrko, P., Šalăt, T. & Wilczynski, W. 2000. I-convergence, real analysis exchange 26(2): 669-686.
Kumar, V. 2007. On I and - convergence of double sequences, Mathematical Communications 12: 171-181.
Lascardies, C. G. 1971. A study of certain sequence spaces of Maddox and generalization of a theorem of Iyer, Pacific Journal Mathematics 38(2): 487-500.
Lascardies, C. G. 1983. On the equivalence of certain sets of sequences, Indian Journal of Mathematics 25(1): 41-52.
Maddox, I. J. 1968. Paranormed sequence spaces generated by infinite matrices, Proceedings of Cambridge Philosophical Society 64: 335-340.
Morciz, F. 1991. Extension of the spaces c and from single to double sequences, Acta Mathematica Hungarica 57(1-2): 129-136.
Morciz, F. & Rhoades, B. E. 1988. Almost convergence of double sequences and strong regularity summability matrices, Mathematical Proceedings of Cambridge Philosophical Society 104: 283-294.
Nabin, A., Pehliven, S. & Gürdal, M. 2007. On I-Canchy sequences, Taiwanese Journal of Mathematics 11(2): 569-76.
Nakano, H. 1951. Modular sequence spaces, Proceedings of Japan Academy 27: 508-512.
Pringsheim, A. 1900. Zur theorie der zweifach unendlichen zahlenfolgen, Mathematical Annals Society 53: 289-321.
Robison, G. M. 1926. Divergent double sequences and series, American Mathematical Society Translations 28: 50-73.
Šalăt, T., Tripathy, B. C. & Ziman, M. 2004. On some properties of I - convergence, Tatra Mountain Mathematical Publications 28: 279-286.
Šalăt, T., Tripathy, B. C. & Ziman, M. 2005. On I - convergence field, Italian Journal of Pure & Applied Mathematics 17: 45-54.
Savas, E. 2010. -strongly summable sequences in 2-normed spaces defined by ideal convergence and an Orlicz function, Applied Mathematics & Computations 217: 271-276.
Simons, S. 1965. The spaces ( ) and m ( ), Proceedings of London Mathematical Society 15: 422-436.
Tripathy, B. C. 2003. Statistical convergence of double sequences, Tamkang Journal of Mathematics 34(3): 231-237.
Tripathy, B. C. & Hazarika, B. 2009. Paranorm I-convergent sequence spaces, Mathematica Slovaca 59(4): 485-494.
Tripathy, B. C. & Hazarika, B. 2011. I-monotonic and I-convergent sequences, Kyungpook Mathematics Journal 51: 233-239, DOI 10.5666/KMJ.2011.51.2.233
Tripathy, B. K. & Tripathy, B. C. 2005. On I-convergent double sequences, Soochow Journal of Mathematics 31(4):549-560.