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Some strongly almost summable sequence spaces

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Treść / Zawartość
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Języki publikacji
EN
Abstrakty
EN
In the present paper we introduce some strongly almost summable sequence spaces using ideal convergence and Musielak-Orlicz function M = (Mk) in n-normed spaces. We examine some topological properties of the resulting sequence spaces.
Rocznik
Tom
Strony
171--183
Opis fizyczny
Bibliogr. 30 poz.
Twórcy
autor
  • Department of Mathematics, Model Institute of Engineering & Technology, Kot Bhalwal, Jammu-181122, J&K, India
autor
  • Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey
Bibliografia
  • [1] S. Banach, Theorie Operations Linearies, Chelsea Publishing Co., New York 1955.
  • [2] P. Das, P. Kostyrko, W. Wilczyński and P. Malik, I and I* convergence of double sequences, Math. Slovaca 58 (2008) 605-620.
  • [3] P. Das, P. Malik, On the statistical and I-variation of double sequences, Real Anal. Exchange 33 (2007-2008) 351-364.
  • [4] A. Esi, Some new sequence spaces defined by a sequence of moduli, Turk. J. Math. 21 (1997) 61-68.
  • [5] A. Esi, Strongly [V2, λ2, M, p]-summable double sequence spaces defined by Orlicz function, Int. J. Nonlinear Anal. Appl. 2 (2011) 110-115.
  • [6] S. Gähler, Linear 2-normietre Rume, Math. Nachr. 28 (1965), 1-43.
  • [7] M. Gurdal, S. Pehlivan, Statistical convergence in 2-normed spaces, Southeast Asian Bull. Math. 33 (2009) 257-264.
  • [8] H. Gunawan, On n-inner product, n-norms, and the Cauchy-Schwartz inequality, Sci. Math. Jpn. 5 (2001) 47-54.
  • [9] H. Gunawan, The space of p-summable sequence and its natural n-norm, Bull. Aust. Math. Soc. 64 (2001) 137-147.
  • [10] H. Gunawan, M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27 (2001) 631-639.
  • [11] P. Kostyrko, T. Salat and W. Wilczyński, I-convergence, Real Anal. Exchange 26 (2000) 669-686.
  • [12] G.G. Lorentz, A contribution to the theory of divergent series, Acta Math. 80 (1948) 167-190.
  • [13] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10 (1971) 345-355.
  • [14] L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Mathematics 5, Departamento de Matemática, Universidade Estadmal de Campinas, Campinas SP Brasil 1989.
  • [15] A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989) 299-319.
  • [16] M. Mursaleen, On some new invariant matrix methods of summability, Quart. J. Math. Oxford 34 (1983) 77-86.
  • [17] M. Mursaleen, A. Alotaibi, On I-convergence in radom 2-normed spaces, Math. Slovaca 61 (2011) 933-940.
  • [18] M. Mursaleen, A.K. Noman, On some new sequence spaces of non absolute type related to the spaces lp and l∞ I, Filomat 25 (2011) 33-51.
  • [19] M. Mursaleen, A.K. Noman, On some new sequence spaces of non absolute type related to the spaces lp and l∞ II, Math. Commun. 16 (2011) 383-398.
  • [20] M. Mursaleen, S.A. Mohiuddine and O.H.H. Edely, On ideal convergence of double sequences in intuitioistic fuzzy normed spaces, Comput. Math. Appl. 59 (2010) 603-611.
  • [21] M. Mursaleen, S.A. Mohiuddine, On ideal convergence of double sequences in probabilistic normed spaces, Math. Reports 64 (2010) 359-371.
  • [22] M. Mursaleen, S.A. Mohiuddine, On ideal convergence in probabilistic normed spaces, Math. Slovaca 62 (2012) 49-62.
  • [23] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034, Springer-Verlag Berlin Heidelberg 1983.
  • [24] K. Raj, S.K. Sharma, Some sequence spaces in 2-normed spaces defined by Musielak-Orlicz function, Acta Univ. Sapientiae Math. 3 (2011) 97-109.
  • [25] K. Raj, S.K. Sharma, Some generalized difference double sequence spaces defined by a sequence of Orlicz-function, CUBO A Mathematical Journal 14 (2012) 167-190.
  • [26] K. Raj, S.K. Sharma, Some multiplier sequence spaces defined by a Musielak-Orlicz function in n-normed spaces, New Zealand J. Math. 42 (2012) 45-56.
  • [27] W. Raymond, Y. Freese and J. Cho, Geometry of Linear 2-Normed Spaces, N. Y. Nova Science Publishers, Huntington 2001.
  • [28] A. Sahiner, M. Gurdal, S. Saltan and H. Gunawan, Ideal convergence in 2-normed spaces, Taiwanese J. Math. 11 (2007) 1477-1484.
  • [29] B.C. Tripathy, B. Hazarika, Some I-convergent sequence spaces defined by Orlicz functions, Acta Mathematicae Applicatae Sinica 27 (2011) 149-154.
  • [30] A. Wilansky, Summability Through Functional Analysis, North-Holland Math. Stud. 85, Elsevier Science Publishers B.V. 1984.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ed1ce15c-92dc-403f-9192-28f55b1da5b9
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