On some spaces of Cesàro sequences of fuzzy numbers associated with λ-convergence and Orlicz function

K. Raj; S. Pandoh

doi:10.2478/ausm-2019-0013

Abstract

In the present paper we shall introduce some generalized difference Cesàro sequence spaces of fuzzy real numbers defined by Musielak-Orlicz function and -convergence. We make an e ort to study some topological and algebraic properties of these sequence spaces. Furthermore, some inclusion relations between these sequence spaces are establish.

References

[1] M. Et, R. Çolak, On generalized difference sequence spaces, Soochow J. Math., 21 (1995), 377–386.
Search in Google Scholar Back to article
[2] M. Et, On some generalized Cesàro difference sequence spaces, Istanb. Univ. Fen Fak. Mat. Fiz. Astron. Derg., 55-56 (1996-1997), 221–229.
Search in Google Scholar Back to article
[3] P. K. Kamthan, M. Gupta, Sequence spaces and series, Marcel Dekker, New York, 1981.
Search in Google Scholar Back to article
[4] H. Kızmaz, On certain sequence spaces, Canad. Math. Bull., 24 (1981), 169–176.10.4153/CMB-1981-027-5
Search in Google Scholar Back to article
[5] J. Lindenstrauss, L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10 (1971), 379–390.10.1007/BF02771656
Search in Google Scholar Back to article
[6] J. Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034, Springer Verlag, 1983.10.1007/BFb0072210
Search in Google Scholar Back to article
[7] M. Matloka, Sequences of fuzzy numbers, BUSEFAL, 28 (1986), 28–37.
Search in Google Scholar Back to article
[8] M. Mursaleen, A. K. Gaur, A. H. Saifi, Some new sequence spaces their duals and matrix transformations, Bull. Calcutta Math. Soc., 88 (1996), 207–212.
Search in Google Scholar Back to article
[9] M. Mursaleen, A. K. Noman, On some new sequence spaces of non absolute type related to the spaces ℓ_∞ and ℓ_∞ I, Filomat, 25 (2011), 33–51.10.2298/FIL1102033M
Search in Google Scholar Back to article
[10] M. Mursaleen, A. K. Noman, On some new sequence spaces of non absolute type related to the spaces ℓ_∞ and ℓ_∞ II, Math. Commun., 16 (2011), 383–398.
Search in Google Scholar Back to article
[11] S. A. Mohiuddine, A. Alotaibi, Some spaces of double sequences obtained through invariant mean and related concepts, Abstr. Appl. Anal., Volume 2013, Article ID 507950, 11 pages (2013).10.1155/2013/507950
Search in Google Scholar Back to article
[12] P. N. Ng, P. Y. Lee, Cesàro sequence spaces of non absolute type, Comment. Math., 20 (1978), 429–433.
Search in Google Scholar Back to article
[13] C. Orhan, Cesàro difference sequence spaces and related matrix transformations, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat., 32 (1983), 55–63.
Search in Google Scholar Back to article
[14] K. Raj, S. K. Sharma, Some difference sequence spaces defined by Musielak-Orlicz functions, Math. Pannon., 24 (2013), 33–4310.3103/S1055134414030067
Search in Google Scholar Back to article
[15] K. Raj, A. Gupta, Multiplier sequence spaces of fuzzy numbers defined by Musielak-Orlicz function, J. Math. Appl., 35 (2012), 69–81.10.7862/rf.2012.6
Search in Google Scholar Back to article
[16] K. Raj, A. Kumar, S. K. Sharma, On some sets of fuzzy difference sequences defined by a sequence of Orlicz function, Int. J. Appl. Math., 24 (2011), 795–805.
Search in Google Scholar Back to article
[17] K. Raj, S. Pandoh, Some sequence spaces of fuzzy numbers for Orlicz functions and partial metric, Kochi J. Math., 11 (2015), 13–33.
Search in Google Scholar Back to article
[18] W. H. Ruckle, FK spaces in which the sequence of coordinates vectors is bounded, Canad. J. Math., 25 (1973), 973–978.10.4153/CJM-1973-102-9
Search in Google Scholar Back to article
[19] B. C. Tripathy, A. Esi, A new type of difference sequences spaces, Int. J. Sci. Tech., 1 (2006), 11–14.
Search in Google Scholar Back to article
[20] B. C. Tripathy, A. Esi, B. K. Tripathy, On a new type of generalized difference Cesàro sequence spaces, Soochow J. Math., 31 (2005), 333–340.
Search in Google Scholar Back to article
[21] B. C. Tripathy, S. Borogohain, Generalised difference Cesàro sequence spaces of fuzzy real numbers defined by Orlicz function, arXiv:1506. 05453v1 [math. FA].10.1155/2011/216414
Search in Google Scholar Back to article
[22] B. K. Tripathy, S. Nanda, Absolute value of fuzzy real numbers and fuzzy sequnce spaces, J. Fuzzy Math., 8(2000), 883–892.
Search in Google Scholar Back to article
[23] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338–353.10.1016/S0019-9958(65)90241-X
Search in Google Scholar Back to article

On some spaces of Cesàro sequences of fuzzy numbers associated with λ-convergence and Orlicz function

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