On the class of $m(\phi)$ bounded variation sequences of fuzzy real numbers
Problemy analiza, Tome 14 (2025) no. 1, pp. 61-76.

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In this article, we introduce the sequence space $bv(\phi, M, p)$, for $1\leq p\infty$ of fuzzy real numbers. We verify and establish some algebraic and topological properties like solidness, monotonicity, convergence-free etc. and prove some inclusion relations of this class of sequences.
Keywords: Orlicz function, bounded variation, fuzzy real number, solid, monotonicity, convergence-free.
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S. J. Boruah; A. J. Dutta. On the class of $m(\phi)$ bounded variation sequences of fuzzy real numbers. Problemy analiza, Tome 14 (2025) no. 1, pp. 61-76. http://geodesic.mathdoc.fr/item/PA_2025_14_1_a3/

[1] Altinok H., Altin Y., Et M., “Lacunary almost statistical convergence of fuzzy numbers”, Thai J. Math., 2:2 (2004), 265–274 | MR | Zbl

[2] Altinok H., Colak R., “Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers”, Iran. Jour. Fuzzy Syst., 11:5 (2014), 39–46 | DOI | MR | Zbl

[3] Basar F., Altay B., Mursaleen M., “Some generalizations of the spaces $bv_p$ of $p$-bounded variation sequences”, Nonlinear Anal. TMA, 68 (2008), 273–287 | DOI | MR | Zbl

[4] Kizmaz H., “On certain sequence spaces”, Canad. Math. Bull., 24:2 (1981), 169–176 | DOI | MR | Zbl

[5] Lindenstrauss J., Tzafriri L., “On Orlicz sequence spaces”, Israel Jour. Math., 10 (1971), 379–390 | DOI | MR | Zbl

[6] Maligranda L., Orlicz spaces and Interpolation, Seminars in Mathematics, 5, Polish Academy of Science, Poland, 1989 | MR

[7] Matloka M., “Sequence of fuzzy numbers”, Busefal, 28 (1986), 28–37 | Zbl

[8] Musielak J., Orlicz Spaces and Modular Spaces, Lecture Notes in Math., 1034, Springer, Berlin-Heidelberg, 1983 | DOI | MR | Zbl

[9] Rath D., Tripathy B. C., “Characterization of certain matrix operators”, Jour. Orissa Math. Soc., 8 (1989), 121–134

[10] Sargent W. L. C., “Some sequence spaces related to the $\ell^p$ spaces”, J. Lond. Math. Soc., 35 (1960), 161–171 | DOI | MR | Zbl

[11] Sava{ş} E., “On strongly $\lambda$-summable sequences of fuzzy numbers”, Inform. Sci., 125 (2000), 181–186 | DOI | MR | Zbl

[12] Tripathy B. C., Baruah A., “New type of difference sequence spaces of fuzzy real numbers”, Math. Model. Anal., 14:3 (2009), 391–397 | DOI | MR | Zbl

[13] Tripathy B. C., Borgohain S., “Sequence Space $m(M,\phi)^F$ of Fuzzy Real Numbers Defined by Orlicz Functions with Fuzzy Metric”, Kyungpook Math. Jour., 53 (2013), 319–332 | DOI | MR | Zbl

[14] Tripathy B. C., Braha N. L., Dutta A. J., “A new class of fuzzy sequences related to the $\ell_p$ space defined by Orlicz function”, Jour. Intel. Fuzzy Syst., 26 (2014), 1273–1278 | DOI | MR | Zbl

[15] Tripathy B. C., Das P. C., “On the class of fuzzy number sequences $bv_p^F$”, Songklanakarin J. Sci. Technol., 41:4 (2019), 934–941

[16] Tripathy B. C., Dutta A. J., “Bounded variation double sequence space of fuzzy real numbers”, Comput. Math. Appl., 59:2 (2010), 1031–1037 | DOI | MR | Zbl

[17] Tripathy B. C., Dutta A. J., “Lacunary bounded variation sequence of fuzzy real numbers”, Jour. Intel. Fuzzy Syst., 24 (2013), 185–189 | DOI | MR | Zbl

[18] Tripathy B. C., Esi A., “A new type of difference sequence spaces”, Int. Jour. Sci. Tech., 1:1 (2006), 11–14

[19] Tripathy B. C., Esi A., Tripathy B. K., “On a new type of generalized difference Cesäro sequence spaces”, Soochow Jour. Math., 31:3 (2005), 333–340 | MR | Zbl

[20] Tripathy B. C., Sen M., “On a new class of sequences related to the space $\ell_p$”, Tamkang J. Math., 33:2 (2002), 167–171 | DOI | MR | Zbl

[21] Zadeh L. A., “Fuzzy sets”, Inform. Control, 8:3 (1965), 338–353 | DOI | MR | Zbl