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Abstrakty
We introduce generalized double lacunary Zweier convergent sequence spaces over n-normed spaces via a sequence of Orlicz functions. We alsomake an e×ort to study some topological properties and inclusion relations between these spaces. Furthermore, we study the concept of double lacunary statistical Zweier convergence over n-normed spaces.
Wydawca
Czasopismo
Rocznik
Tom
Strony
185--207
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
autor
- School of Mathematics Shri Mata Vaishno Devi University, Katra-182320, J& K, India
autor
- School of Mathematics Shri Mata Vaishno Devi University, Katra-182320, J& K, India
Bibliografia
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- [3] K. Ebadullah, A. Esi, N. Khan, V. A. Khan, and M. Shafiq, On paranorm Zweier I-convergent sequence spaces, J. Math. (2013), Art. ID 613501, 6.
- [4] K. Ebadullah, A. Esi, V. A. Khan, and M. Shafiq, On some Zeweir I-convergent sequence spaces defined by a modulus function, Afr. Mat. 26 (2015), no. 1-2,115-125, DOI 10.1007/s13370-013-0186-y.
- [5] O. H. Edely and M. Mursaleen, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), no. 1, 223-231, DOI 10.1016/j.jmaa.2003.08.004.
- [6] A. Esi and A. Sapsizoglu, On some lacunary a-strong Zweier convergent sequence spaces, Romai J. 8 (2012), no. 2, 61-70.
- [7] A. Esi and M. Acikgoz, On some double lacunary strong Zweier convergent sequence spaces, An. Univ. Craiova Ser. Mat. Inform. 40 (2013), 121-127.
- [8] M. Et and R. Çolak, On generalized difference sequence spaces, Soochow J. Math. 21 (1995), 377-386.
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- [10] S. Gähler, Lineare 2-Normierte Räume, Math. Nachr. 28 (1965), 1-43.
- [11] H. Gunawan, On n-innerproduct, n-norms, and the Cauchy-Schwartz inequality, Sci. Math. Jpn. 5 (2001), 47-54.
- [12] H. Gunawan, The space of p-summable sequences and its natural n-norm, Bull. Aust. Math. Soc. 6 (2001), 137-147, DOI 10.1017/S0004972700019754.
- [13] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci. 27 (2001), 631-639, DOI 10.1155/S0161171201010675.
- [14] A. Gupta, K. Raj, and S. K. Sharma, Some difference paranormed sequence spaces over n-normed spaces defined by Musielak-Orlicz function, Kyungpook Math. J. 54 (2014), 73-86, DOI 10.5666/KMJ.2014.54.1.73.
- [15] G. H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc. 19 (1917), 86-95, DOI 10.1112/plms/s2-1.1.124.
- [16] H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24 (1981), 169-176, DOI 10.4153/CMB-1981-027-5.
- [17] J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379-390, DOI 10.1007/BF02771656.
- [18] L. Maligranda, Orlicz Spaces and Interpolation, Seminars in Mathematics, vol. 5, Universidade Estadual de Campinas, Departamento de Matemática, Campinas 1989.
- [19] A. Misiak, n-inner product spaces, Math. Nachr. 140 (1989), 299-319, DOI 10.1002/mana.19891400121.
- [20] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics, vol. 1034, Springer Verlag 1983, DOI 10.1007/BFb0072210.
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- [22] K. Raj and S. K. Sharma, Some multiplier double sequence spaces, Acta Math. Vietnam. 37 (2012), 391-406.
- [23] K. Raj and S. K. Sharma, Some difference sequence spaces defined by Musielak-Orlicz functions, Math. Pan- non. 24 (2013), 33-43.
- [24] K. Raj and S. K. Sharma, Double sequence spaces over n-normed spaces, Arch. Math. (Brno) 50 (2014), 7-18, DOI 10.5817/AM2014-2-65.
- [25] E. Sava§ and R. F. Patterson, On some double almost lacunary sequence spaces defined by Orlicz functions, Filomat 19 (2005), 35-44.
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- [27] E. Savaş, On some new double lacunary sequence spaces via Orlicz function, J. Comput. Anal. Appl. 11 (2009), no. 3, 423-430.
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Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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