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On Some Lacunary Generalized Difference Sequence Spaces of Invariant Means Defined by a Sequence of Modulus Functions

Gülcan Atici|Çiğdem Asma Bektaş
경북대학교 자연과학대학 수학과|2011.12|Kyungpook Mathematical Journal|제51권 제4호|pp. 385-393

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참고문헌

키워드

modulus functionlacunary sequenceInvariant meanDifference sequence spaces
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초록

The aim of this paper is to introduce and study the sequence spaces [w, θ, F, p, q]∞(Δ^m_v), [w, θ, F, p, q]₁∞(Δ^m_v) and [w, θ, F, p, q]_0∞(Δ^m_v) which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli F = (f_k). We establish some inclusion relations between these spaces under some conditions.

Abstract

The aim of this paper is to introduce and study the sequence spaces [w, θ, F, p, q]∞(Δ^m_v), [w, θ, F, p, q]₁∞(Δ^m_v) and [w, θ, F, p, q]_0∞(Δ^m_v) which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli F = (f_k). We establish some inclusion relations between these spaces under some conditions.

참고문헌 (29)

  1. S. Banach, "Theorie des Operations Lineaires" (1932), PWN
  2. Ç . A. BektaS, "Generalized difference sequences defined by a sequence of moduli", Soochow J. Math, 29(2), pp.215~220 (2003)
  3. Ç . A. BektaS, "Generalized strongly almost summable difference sequences of order m defined by a sequence of moduli", Demonstratio Mathematica, 40(3), pp.581~591 (2007)
  4. M. Et, "Spaces of Ces`aro difference sequences of order r defined by a Modulus function in a locally convex space", Taiwanese Journal of Mathematics, 10(4), pp.865~879 (2006)
  5. M. Et, "On some classes of sequences defined by sequences of Orlicz functions", Mathematical Inequalities and Applications, 9(2), pp.335~342 (2006)
  6. M. Et, "On some generalized difference sequence spaces", Soochow J. Math, 21, pp.377~386 (1995)
  7. M. Et, "On Köthe-Toeplitz duals of generalized difference sequence spaces", Bull. Malaysian Math. Sc. Soc, 23(2), pp.25~32 (2000)
  8. M. Et, "Lacunary strongly almost summable sequences", Studia Univ. BabeS¸-Bolyai Mathematica, 4, pp.29~38 (2008)
  9. A. R. Freedman, "Some Ces`aro-type summability spaces", Proc. London Math. Soc, 37(3), pp.508~520 (1978)
  10. H. Kizmaz, "On certain sequence spaces", Canad. Math. Bull, 24, pp.169~176 (1981)
  11. G. G. Lorentz, "A contribution to the theory of divergent sequences", Acta Math, 80, pp.167~190 (1948)
  12. I. J. Maddox, "Elements of Functional Analysis" (1970), Cambridge University Press
  13. I. J. Maddox, "Sequence spaces de ned by a modulus", Math. Proc. Cambridge Philos. Soc, 100, pp.161~166 (1986)
  14. S. Pehlivan, "Lacunary strong convergence with respect to a sequence of modulus functions", Comment Math. Univ. Carolin, 36, pp.69~76 (1995)
  15. W. H. Ruckle, "FK spaces in which the sequence of coordinate vectors is bounded", Canad. J. Math, 25, pp.973~978 (1973)
  16. P. Schaefer, "Infinite matrices and invariant means", Proc. Amer. Math. Soc, 36, pp.104~110 (1972)
  17. B. C. Tripathy, "On generalized statistically convergent sequences", Indian Journal of Pure and Applied Mathematics, 32(11), pp.1689~1694 (2001)
  18. B. C. Tripathy, "On generalized difference paranormed statistically convergent se-quences", Indian Journal of Pure and Applied Mathematics, 35(5), pp.655~663 (2004)
  19. B. C. Tripathy, "On a class of generalized lacunary difference sequence spaces defined by Orlicz function", Acta Mathematica Applicata Sinica, 20(2), pp.231~238 (2004)
  20. B. C. Triapthy, "On a class of vector valued sequences associated with multiplier sequences", Acta Mathematica Applicata Sinica, 20(3), pp.487~494 (2004)
  21. B. C. Tripathy, "Characterization of some matrix classes involving para-normed sequence spaces", Tamkang Journal of Mathematics, 37(2), pp.155~162 (2006)
  22. B. C. Tripathy, "Statistically convergent difference double sequence spaces", Acta Mathematica Sinica, 24(5), pp.737~742 (2008)
  23. B. C. Tripathy, "Generalized difference sequences spaces on semi-normed spaces defined by Orlicz functions", Mathematica Slovaca, 58(3), pp.315~324 (2008)
  24. B. C. Tripathy, "Difference sequence space m(M; ϕ;Δn m; p)F of fuzzy real numbers", Mathematical Modelling and Analysis, 13(4), pp.577~586 (2008)
  25. Binod Chandra Tripathy, "Some Difference Double Sequence Spaces Defined By Orlicz Function", Kyungpook Mathematical Journal, 48(4), pp.613~622 (2008), 경북대학교 자연과학대학 수학과
  26. B. C. Tripathy, "Vector valued double sequence spaces defined by Orlicz function", Mathematica Slovaca, 59(6), pp.767~776 (2009)
  27. B. C. Tripathy, "New type of difference sequence spaces of fuzzy real numbers", Mathematical Modelling and Analysis, 14(3), pp.391~397 (2009)
  28. Binod Chandra Tripathy, "On Some New Paranormed Difference Sequence Spaces De- fined by Orlicz Functions", Kyungpook Mathematical Journal, 50(1), pp.59~69 (2010), 경북대학교 자연과학대학 수학과
  29. A. Wilansky, "Functional Analysis" (1964), Blaisdell Publishing Company

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