In this article, we introduce and study deferred Cesàro statistical convergence in measure by virtue of sequences of fuzzy valued measurable functions. We define inner and outer deferred Cesàro statistical convergence in measure for sequences of fuzzy valued measurable functions and exhibit that in a finite measurable set, both types of convergence are equal. Finally, we prove the new version of Egorov’s theorem by using deferred Cesàro statistical convergence for the sequences of fuzzy valued functions in finite measurable spaces.
FastH. (1951). Sur la convergence statistique. Colloquium Mathematicum, 2, 241–244.
5.
GadjievA. D.OrhanC. (2002). Some approximation theorems via statistical convergence. Rocky Mountain Journal of Mathematics, 32(1), 129–138.
6.
HazarikaB.AlotaibiA.MohiuddineS. A. (2020). Statistical convergence in measure for double sequences of fuzzy-valued functions. Soft Computer, 44, 6613–6622.
7.
HazarikaB.SavaşE. (2011). Some -convergent summable difference sequence spaces of fuzzy real numbers defined by a sequence of orlicz functions. Mathematical and Computer Modelling: An International Journal, 54, 2986–2998.
8.
JasrotiaS.SinghU. P.RajK. (2020). Applications of statistical convergence of order in difference sequence spaces of fuzzy numbers. Journal of Intelligent & Fuzzy Systems, 40(3), 4695–4703. https://doi.org/10.3233/JIFS-201539
9.
MatlokaM. (1986). Sequences of fuzzy numbers. Busefal, 28, 28–37.
10.
MohiuddineS. A.AlotaibiA.MursaleenM. (2012). Statistical convergence of double sequences in locally solid riesz spaces. Abstract and Applied Analysis, 2012(1), 1–9.
11.
MohiuddineS. A.LohaniQ. M. D. (2009). On generalized statistical convergence in intuitionistic fuzzy normed space. Chaos Solitons Fractals, 42(3), 1731–1737.
12.
MursaleenM.MohiuddineS. A. (2009). Statistical convergence of double sequences in intuitionistic fuzzy normed spaces. Chaos Solitons Fractals, 41(5), 2414–2421.
13.
NandaS. (1989). On sequences of fuzzy numbers. Fuzzy Sets and Systems, 33, 123–126.
14.
NegoitaC. V.RalescuD. (1989). On sequences of fuzzy numbers. Fuzzy Sets and Systems, 33, 123–126.
15.
NurayF.SavaşE. (1995). Statistical convergence of sequences of fuzzy numbers. Mathematica Slovaca, 45(3), 269–273.
16.
RajK.JamwalS.SharmaS. K. (2012). Multiplier generalized double sequence spaces of fuzzy numbers defined by sequence of orlicz functions. International Journal of Pure and Applied Mathematics, 78(4), 509–522.
17.
RajK.PandohS. (2019). On some spaces of cesàro sequences of fuzzy numbers associated with convergence and orlicz function. Acta Universitatis Sapientiae, Mathematica, 11(1), 156–171.
18.
RathD.TripathyB. C. (1996). Matrix maps on sequence spaces associated with sets of integers. Indian Journal of Pure and Applied Mathematics, 27(2), 197–206.
19.
SavaşR. (2020). On asymptotically deferred statistical equivalent measurable functions. Journal of Classical Analysis, 16(2), 141–147.
20.
SavaşR. (2020). Some inclusion theorems related to asymptotically deferred statistical equivalent measurable functions. Punjab University Journal of Mathematics, 52(12), 1–7.
21.
SavaşR. (2022). Rates of asymptotically statistical equivalents of measurable function. Mathematical Methods in the Applied Sciences, 45(18), 12119–12124.
22.
SavaşE.MursaleenM. (2004). On statistically convergent double sequences of fuzzy numbers. Information Sciences, 162, 183–192.
23.
SchoenbergI. J. (1959). The integrability of certain functions and related summability methods. American Mathematical Monthly, 66(5), 361–775.
24.
TripathyB. C.NandaS. (2000). Absolute value of fuzzy real number and fuzzy sequence spaces. Journal of Fuzzy Mathematics, 8, 883–892.
25.
ZadehL. A. (1965). Fuzzy set. Information and Computation, 8, 338–353.
