Some classes of ideal convergent difference sequence spaces of fuzzy numbers defined by Orlicz function

• Autorzy: Hazarika B
• Języki publikacji: EN

Abstrakty

EN

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In [25], Kostyrko et. al introduced the concept of ideal convergence as a sequence (x_k) of real numbers is said to be I-convergent to a real number l, if for each Ɛ > 0 the set {k N : |x_k - l| > Ɛ} belongs to I. In this article we introduce the concept of ideal convergent sequence of fuzzy numbers using difference operator and Orlicz functions and study their basic facts. Also we investigate the different algebraic and topological properties of these classes of sequences.

Słowa kluczowe

EN

ideal; I-convergence; fuzzy number; normal space; symmetric space; difference space

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 52
• Strony: 45--63
• Opis fizyczny: Bibliogr. 45 poz.

Twórcy

autor

Hazarika B

• Department of Mathematics Rajiv Gandhi University Rono Hills, Doimukh-791 112 Arunachal Pradesh, India

Bibliografia

• [1] Anastassiou G.A., Fuzzy approximation by fuzzy convolution type operators, Compt. Math. Appl., 48(2004), 369-386.
• [2] Barros L.C., Bassanezi R.C., Tonelli P.A., Fuzzy modelling in population dynamics, Ecol. Model, 128(2000), 27-33.
• [3] Burgin M., Neoclassical analysis: fuzzy continuity and convergence, Fuzzy Sets and Systems, 75(1995), 291-299.
• [4] Colak R., Et M., On some generalized difference sequence spaces and related matrix transformations, Hokkaido Math. J., 26(3)(1997), 483-492.
• [5] Colak R., Altinok H., Et M., Generalized difference sequences of fuzzy numbers, Chaos, Solitions, Fractals, 40(2009), 1106-1117.
• [6] Duman O., Ali M., Özarslan, Erkuş-Duman E., Rate of Ideal convergence for approximation operators, Mediterr. J. Math., 7(2010), 111-121.
• [7] Esi A., Hazarika B., A-ideal convergence in intuitionistic fuzzy 2-nor- med linear space, Journal of Intelligent and Fuzzy Systems, 24(4)(2013), 725-732, DOI: 10.3233/ IFS-2012-0592.
• [8] Esi A., Hazarika B., Lacunary summable sequence spaces of fuzzy numbers defined by ideal convergence and an Orlicz function, Afrika Matematika, 25(2014), 331-343, DOI: 10.1007/s13370-012-0117-3.
• [9] Et M., Basarir M., On some new generalized difference sequence spaces, Period Math. Hungar, 35(3)(1997), 169-175.
• [10] Et M., Colak R., On some generalized difference sequence spaces, Soochow J. Math., 21(4)(1995), 377-386.
• [11] Et M., Altin Y., Altinok H., On almost statistical convergence difference sequences of fuzzy numbers, Math. Model. Anal., 10(4)(2005), 345-352.
• [12] Fast H., Sur la convergence statistique, Colloq. Math., 2(1951), 241-244.
• [13] Giles R., A computer programming for fuzzy reasoning, Fuzzy Sets and Systems, 4(1980), 221-234.
• [14] Hazarika B., Sayas E., Some I-convergent lambda-summable difference sequence spaces of fuzzy real numbers defined by a sequence of Orlicz functions, Math. Comp. Model., 54 (11-12)(2011), 2986-2998, DOI No: 10.1016/j.mcm.2011.07.026.
• [15] Hazarika B., On paranormed ideal convergent generalized difference strongly summable sequence spaces defined over n-normed spaces, ISRN Math. Anal., 2011(2011), 17 pages, DOI:10.5402/2011/317423.
• [16] Hazarika B., On fuzzy real valued generalized difference I-convergent sequence spaces defined by Musielak-Orlicz function, Journal of Intelligent and Fuzzy Systems, 25(1)(2013), 9-15, DOI: 10.3233/IFS-2012-0609.
• [17] Hazarika B., Fuzzy real valued lacunary I-convergent sequences, Applied Math. Letters, 25(3)(2012), 466-470.
• [18] Hazarika B., On ideal convergence in topological groups, Scientia Magna, 7(4)(2011), 80-86.
• [19] Hazarika B., Lacunary difference ideal convergent sequence spaces of fuzzy numbers, Journal of Intelligent and Fuzzy Systems, 25(1)(2013), 157-166, DOI: 10.3233/IFS-2012-0622.
• [20] Hazarika B., On generalized difference ideal convergence in random 2-normed spaces, Filomat, 26(6)(2012), 1265-1274.
• [21] Hazarika B., Lacunary generalized difference statistical convergence in random 2-normed spaces, Proyecciones Journal of Mathematics, 31(4)(2012), 373-390.
• [22] Hong L., Sun J.Q., Bifurcations of fuzzy nonlinear dynamical systems, Com-mon. Nonlinear Sci. Numer. Simul., 1(2006), 1-12.
• [23] Kamthan P.K., Gupta M., Sequence Spaces and Series, Marcel Dekkar, 1980.
• [24] Kizmaz H., On certain sequence spaces, Canad. Math. Bull., 24(2)(1981), 169-176.
• [25] Kostyrko P., Šalát T., Wilczyński W., On I-convergence, Real Analysis Exchange, 26(2)(2000-2001), 669-686.
• [26] Krasnoselski M.A., Rutitsky Y.B., Convex functions and Orlicz spaces, Netherlands, Groningen, 1961.
• [27] Kumar V., Kumar K., On the ideal convergence of sequences of fuzzy numbers, Inform. Sci., 178(2008), 4670-4678.
• [28] Lindberg K., On subspaces of Orlicz sequence spaces, Studia Math., 45(1973), 119-146.
• [29] Lindenstrauss J., Tzafriri L., On Orlicz sequence spaces, Israel J. Math., 10(1971), 379-390.
• [30] Matloka M., Sequences of fuzzy numbers, Fuzzy Sets and Systems, 28(1986), 28-37.
• [31] Mursaleen M., Khan M.A., Qamaruddin, Difference sequence spaces defined by Orlicz functions, Demonstratio. Math., 32(1999), 145-150.
• [32] Mursaleen M., Mohiuddine S.A., Nonlinear operators between intuitionistic fuzzy normed spaces and Frechet differentiation, Chaos, Solitons, Fractals, 42(2009), 1010-1015.
• [33] Nanda S., On sequences of fuzzy numbers, Fuzzy Sets and Systems, 33(1989), 123-126.
• [34] Nung N.P., Lee P.Y., Orlicz sequence spaces of a non absolute type, Comment. Math. Univ. St. Publ., 26(2)(1977), 209-213.
• [35] Peeva K., Fuzzy linear systems, Fuzzy Sets and Systems, 49(1992), 339-355.
• [36] Šalát T., Tripathy B.C., Ziman M., On some properties of 1-convergence, Tatra Mt. Math. Publ., 28(2004), 279-286.
• [37] Šalát T., Tripathy B.C., Ziman M., On 1-convergence field, Italian J. Pure Appl. Math., 17(2005), 45-54.
• [38] Savaş E., Δm-strongly summable sequences in 2-normed spaces defined by ideal convergence and an Orlicz function, Appl. Math. and Comp., 217(2010), 271-276.
• [39] Tripathy B.C., Mahanta S., On I-acceleration convergence of sequences, Jour. of The Franklin Inst., 347(2010), 591-598.
• [40] Tripathy B.C., Hazarika B., Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4)(2009), 485-494.
• [41] Tripathy B.C., Hazarika B., Some I-convergent sequence spaces defined by Orlicz function, Acta Appl. Math. Sinica, 27(1)(2011), 149-154, DOI: 10.1007/s10255-011-0048-z.
• [42] Tripathy B.C., Hazarika B., I-monotonic and I-convergent sequences, Kyungpook Math. J, 51(2011), 233-239, DOI 10.5666/KMJ.2011.51.2.233.
• [43] Tripathy B.C., Hazarika B., I-convergent sequence spaces associated with multiplier sequences, Math. Ineq. Appl., 11(3)(2008), 543-548.
• [44] Tripathy B.C., Esi A., Tripathy B.K., On a new type of generalized difference Cesaro sequence spaces, Soochow J. Math., 31(2005), 333-340.
• [45] Zadeh L.A., Fuzzy sets, Information and Control, 8(1965), 338-353.