Abstract
In this paper, we introduce new difference sequence spaces combining with de la Vallee-Poussin mean using by a sequence of modulus functions and ϕ -functions. We also studied connections between statistically convergence related with this space.
Keywords Difference sequence, Modulus function, ϕ -function, De la Vallee-Poussin means, Statistical convergence
Mathematics Subject Classification (2000) 46A45, 40F05, 46A80
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1. Bataineh, Ahmad H.A., Azar, L. E.: On new difference sequence spaces defined by a sequence of Orlicz functions, J. Inst. Math. Comput. Sci. Math. Ser., 16 (2003), 51–56
2. Bilgin, T.: Some new difference sequence spaces defined by an Orlicz functions, Filomat, 17 (2003), 1–8
3. Bilgin, T.: On statistical convergence, An. Univ. Timisoara Ser. Math. Inform., 32 (1) (1994), 3–7.
4. Et, M., Çolak, R.: On Some Generalized Difference Sequence Spaces, Soochow Journal of Math., 21 (4) (1995), 377–386
5. Et, M., Başarır, M.: On Some New Generalized Difference Sequence Spaces, Period. Math. Hung., 35 (1997), 169–175
6. Et, M., Altın, Y., Altınok, H.: On some generalized difference sequence spaces defined by a modulus function, Filomat, 17 (2003), 23–33
7. Kızmaz, H.: On Certain Sequence Spaces, Canad. Math. Bull., 24 (1981), 169–176
8. Leindler, L.: Über de la Vale Pounsische Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hung., 16 (1965), 375–378
9. Maddox, I.J.: Spaces of strongly summable sequences, Quart. J. Math., 18 (2) (1967), 345–355
10. Maddox, I.J.: Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc., 100 (1986), 161–166
11. Malkowsky, E., Parashar, S.D.: Matrix transformations in spaces of bounded and convergent difference sequences of order m, Analysis, 17 (1997), 87–97
12. Malkowsky, E., Savaş, E.: Some λ -sequence spaces defined by a modulus, Archivum Mathematicum, 36 (2000), 219–228
13. Pehlivan, S., Fisher, B.: Lacunary strong convergence with respect to a sequence of modulus functions, Comment. Math. Univ. Carolinae, 36 (1) (1995), 71–78
14. Pehlivan, S., Fisher, B.: Some sequence spaces defined by a modulus function, Math. Slovaca, 45 (1994)
15. Ruckle, W.H.: FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25 (1973), 973–978
16. Savaş, E.: On some generalized sequence spaces defined by a modulus, Indian J. Pure and Appl. Math., 30 (5) (1999), 459–464
17. Savaş, E.: On strong σ -convergence in some sequence spaces, (submitted)
18. Waszak, A.: Some remarks on strong convergence in modular spaces of sequences, Fasc. Math., 35 (2005), 151–162
19. Waszak, A.: On the strong convergence in some sequence spaces, Fasc. Math., 73 (2002), 125–137
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Başarir, M., Altundağ, S. Some difference sequence spaces defined by a sequence of ϕ -functions. Rend. Circ. Mat. Palermo 57, 149–160 (2008). https://doi.org/10.1007/s12215-008-0009-4
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DOI: https://doi.org/10.1007/s12215-008-0009-4