On some generalized statistically convergent sequence spaces
Keywords:
Generalized difference sequence space, Musielak-Orlicz function, n − normed space, paranorm, statistical convergence.Abstract
In this paper we construct some generalized new difference statistically convergentsequence spaces defined by a Musielak-Orlicz function over n − normed spaces. Wealso study several properties relevant to topological structures and inclusion relationsbetween these spaces.References
Altin, Y., Et, M. & Tripathy, B. C. 2004. The sequence space on seminormed spaces,
Applied Mathematics and Computation, 154: 423-430.
Bektaş, Ç. A., Et, M. & Çolak, R. 2004. Generalized difference sequence spaces and their dual spaces,
Journal of Mathematical Analysis and Applications, 292: 423-432.
Başarir, M., Konca, S. & Kara, E. E. 2013. Some generalized difference statistically convergent sequence
spaces in 2-normed space, Journal of Inequalities and Applications, 2013: 177.
Başarir, M. & Nuray, F. 1991. Paranormed difference sequence spaces generated by infinite matrices,
Pure & Applied Mathematika Sciences, 34: 87-90.
Başarir, M. & Kayıkçı, M. 2009. On the generalized Bm − Riesz difference sequence space and β −
property, Journal of Inequalities and Applications, Article ID 385029.
Başar, F. & Altay, B. 2003. On the space of sequences of p − bounded variation and related matrix
mappings, Ukrainian Mathematical Journal, 55: 136-147.
Esi, A. 2013. Lacunary strong A − convergent sequence spaces defined by sequences of modulus, Kuwait
Journal of Science, 40: 57-65.
Esi, A., Tripathy, B. C. & Sarma, B. 2007. On some new type generalized difference sequence spaces,
Mathematica Slovaca, 57: 475-482.
Esi, A. & Et, M. 2000. Some new sequence spaces defined by a sequence of Orlicz functions, Indian
Journal of Pure and Applied Mathematics, 31: 967-972.
Et, M. & Çolak, R. 1995. On generalized difference sequence spaces, Soochow Journal of Mathematics,
: 377-386.
Et, M. & Esi, A. 2000. On Köthe - Toeplitz duals of generalized difference sequence spaces, Bulletin of
the Malaysian Mathematical Sciences Society, 23: 25-32.
Et, M., Altin, Y., Choudhary, B. & Tripathy, B. C. 2006. On some classes of sequences defined by
sequences Orlicz functions, Mathematical Inequalities and Applications, 9: 335-342.
Fast, H. 1951. Sur la convergence statistique, Colloquium Mathematicum, 2: 241-244.
Fridy, J. A. 1985. On statistical convergence, Analysis, 5: 301-313.
Gӓhler, S. 1965. Linear 2-normietre Rume, Mathematische Nachrichten, 28: 1-43.
Gunawan, H. 2001a. On n − inner product, n − norms, and the Cauchy-Schwartz inequality, Scientiae
Mathematicae Japonicae, 5: 47-54.
Gunawan, H. 2001b. The space of p − summable sequence and its natural n − norm, Bulletin of the
Australian Mathematical Society, 64: 137-147.
Gunawan, H. & Mashadi, M. 2001. On n − normed spaces, International Journal of Mathematics and
Mathematical Sciences, 27: 631-639.
Kizmaz, H. 1981. On certain sequence spaces, Canadian Mathematical Bulletin, 24: 169-176.
Kirişçi, M. & Başar, F. 2010. Some new sequence spaces derived by the domain of generalized diffrence
matrix, Computers & Mathematics with Applications, 60: 1299-1309.
Lindenstrauss, J. & Tzafriri, L. 1971. On Orlicz sequence spaces, Israel Journal of Mathematics, 10:
-390.
Misiak, A. 1989. n − Inner product spaces, Mathematische Nachrichten, 140: 299-319.
Mursaleen, M. 1996. Generalized spaces of difference sequences, Journal of Mathematical Analysis and
Applications, 203: 738-745.
Maligranda, L. 1989. Orlicz spaces and interpolation, Seminars in Mathematics 5, Polish Academy of
Science.
Musielak, J. 1983. Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034.
Parasher, S. D. & Choudhary, B. 1994. Sequence spaces defined by Orlicz function, Indian Journal of
Pure and Applied Mathematics, 25: 419-428.
Raj, K., Sharma, A. K. & Sharma, S. K. 2011. A sequence space defined by Musielak-Orlicz functions,
International Journal of Pure and Applied Mathematics, 67: 475-484.
Raj, K. & Sharma, S. K. 2012. A new sequence space defined by a sequence of Orlicz functions over
n − normed spaces, Acta Universitatis Palackianae Olomucensis, Facultas Rerum Naturalium,
Mathematica, 51: 89-100.
Raj, K., Sharma, S. K. & Sharma, A. K. 2010. Some difference sequence spaces in n-normed spaces
defined by Musielak-Orlicz function, Armenian journal of Mathematics, 3: 127-141.
Raj, K. & Sharma, S. K. 2013a. Some difference sequence spaces defined by Musielak-Orlicz functions,
Mathematica Pannonica, 24: 33-43.
Raj, K. & Sharma, S. K. 2013b. Some new sequence spaces, Applications and Applied Mathematics, 8:
-613.
Schoenberg, I. J. 1959. The integrability of certain functions and related summability methods, American
Mathematical Monthly, 66: 361-375.
Sen, M. & Roy, S. 2013. On paranormed type fuzzy I-convergent double multiplier sequences, Kuwait
Journal of Science, 40: 1-12.
Tripathy, B. C. & Dutta, H. 2010. On some new paranormed difference sequence spaces defined by
Orlicz functions, Kyungpook Mathematical Journal, 50: 59-69.
Tripathy, B. C., Esi, A. & Tripathy, B. 2005. On a new type of generalized difference Ces`aro sequence
spaces, Soochow Journal of Mathematics, 31: 333-340.
Tripathy, B. C. & Esi, A. 2006. A new type of difference sequence spaces, International Journal of Science
and Technology, 1: 11-14.
Tripathy, B. C. & Mahanta, S. 2003. On a class of sequences related to the lp space defined by Orlicz
functions, Soochow Journal of Mathematics, 29: 379-391.
Tripathy, B. C., Altin, Y. & Et, M. 2008. Generalized difference sequence spaces on seminormed spaces
defined by Orlicz functions, Mathematica Slovaca, 58: 315-324.
Tripathy, B. C. & Dutta, H. 2012. On some lacunary difference sequence spaces defined by sequence of
Orlicz functions and q − lacunary Δn −
m Statistical convergence, Analele Stiintifice ale Universitatii
Ovidius, Seria Matematica, 20: 417-430.
Tripathy, B. C., Sen, M. & Nath, S. 2012a. I − convergence in probabilistic n − normed space, Soft
Computing, 16: 1021-1027, DOI 10.1007/s00500-011-0799-8.
Tripathy, B. C., Baruah, A., Et, M. & Gungor, M. 2012b. On almost statistical convergence of new type
of generalized difference sequence of fuzzy numbers, Iranian Journal of Science and Technology
Transaction A: Science, 36: 147-155.
Tripathy, B. C. & Borgogain, S. 2013. On a class of n − normed sequences related to the − p l space,
Boletim da Sociedade Paranaense de Matemàtica, 31: 167-173.
Wilansky, A. 1984. Summability through functional analysis, North-Holland Mathematics Studies
Zygmund, A. 2011. Trigonometric Series, Cambridge University Press, Cambridge 51: 233-239.