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Abstrakty
In this paper, we introduce some new sequence spaces combining with lacunary sequence, σ-convergence, a sequence of φ-functions and a sequence of modulus functions. We establish some inclusion relations between these spaces under some conditions. Also we studied connections between lacunary (A, φk, σ )-statistically convergence with these spaces.
Czasopismo
Rocznik
Tom
Strony
19--32
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Department of Mathematics Faculty of Science and Arts Sakarya University, 54187, Sakarya, Turkey, basarir@sakarya.edu.tr
Bibliografia
- [1] Lorentz G.G., A contribution to the theory of divergent sequences, Acta Math., 80(1948), 167-190.
- [2] Maddox I.J., Spaces of strongly summable sequences, Quart. J. Math., 18(1967), 345-355.
- [3] Schaefer P., Infinite matrices and invariant means, Proc. Amer. Math. Soc., 36(1972), 104-110.
- [4] Freedman A.R., Sember J.J., Raphael M., Some Cesaro-type summability spaces, Proc. London Math. Soc., 37(3)(1978), 508-520.
- [5] Mursaleen, Matrix transformation between some new sequence spaces, Houston J. Math., 9(1993), 505-509.
- [6] Ruckle W.H., FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978.
- [7] Maddox I.J., Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc., 100(1986), 161-166.
- [8] Pehlivan S., Fisher B., Lacunary strong convergence with respect to a sequence of modulus functions, Comment. Math. Univ. Carolinae, 36(1)(1995), 71-78.
- [9] Bilgin T., On statistical convergence, An. Univ. Timisoara Ser. Math. Inform., 32(1)(1994), 3-7.
- [10] Karakaya V., Şimşek N., On lacunary invariant sequence spaces defined by a sequence of modulus functions, App. Math. And Comp., 156(2004), 597-603.
- [11] Savaş¸ E., On some generalized sequence spaces defined by a modulus, Indian J. Pure and Appl. Math., 30(5)(1999), 459-464.
- [12] Waszak A., Some remarks on strong convergence in modular spaces of sequences, Fasc. Math., 35(2005), 151-162.
- [13] Waszak A., On the strong convergence in some sequence spaces, Fasc. Math., 33(2002), 125-137.
- [14] Başarır M., Altundağ S., Some difference sequence spaces defined by a sequence of ϕ-functions, Rendiconti del Circolo Matematico di Palermo, 57(2008), 149-160.
- [15] Pehlivan S., Fisher B., Some sequence spaces defined by a modulus function, Math. Slovaca, 45(3)(1995), 275–280.
- [16] Kolk E., Mölder A., Inclusion theorems for some sets of sequences defined by ϕ-functions, Math. Slovaca, 54(3)(2004), 267-279.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP3-0002-0063