In this paper, we define the spaces for sequences of fuzzy numbers using generalized difference operator Δm and a lacunary sequence θ and give some relations between them, where β ∈ (0, 1] and p > 0. Furthermore, in the last section of paper, some inclusion theorems are presented related to the spaces and according to modulus function f.
AltinY., EtM. and TripathyB.C., The sequence space on inormed spaces, Appl Math Comput154(2) (2004), 423–430sem.
2.
AltinY., MursaleenM. and AltinokH., Statistical summability (C,1) for sequences of fuzzy real numbers and a Tauberian theorem, J Intell Fuzzy Systems21(6) (2010), 379–384.
3.
AltinokH., Statistical convergence of order β for generalized difference sequences of fuzzy numbers, Journal of Intelligent & Fuzzy Systems26 (2014), 847–856.
4.
AltinokH., AltinY. and IşikM., Statistical convergence and strong p-Cesáro summability of order β in sequences of fuzzy numbers, Iranian J of Fuzzy Systems9(2) (2012), 65–75.
5.
AltinokH., EtM. and ÇolakR., Some remarks on generalized sequence space of bounded variation of sequences of fuzzy numbers, Iranian J of Fuzzy Systems11(5) (2014), 39–46.
6.
AltinokH. and MursaleenM., vartriangle-Statistically boundedness for sequences of fuzzy numbers, Taiwanese J Math15(5) (2011), 2081–2093.
7.
Çanakİ., Tauberian theorems for Cesaro summability of sequences of fuzzy numbers, J Intell Fuzzy Syst27(2) (2014), 937–942.
8.
Çanakİ., On the Riesz mean of sequences of fuzzy real numbers, J Intell Fuzzy Syst26(6) (2014), 2685–2688.
9.
Çanakİ., Some conditions under which slow oscillation of a sequence of fuzzy numbers follows from Cesaro summability of its generator sequence, Iran J Fuzzy Syst11(4) (2014), 15–22.
10.
Çanakİ., Hölder summability method of fuzzy numbers and a Tauberian theorem, Iran J Fuzzy Syst11(4) (2014), 87–93.
11.
ÖnderZ., SezerS.A. and Çanakİ., A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers, J Intell Fuzzy Syst28 (2015), 1403–1409.
12.
ÇolakR., Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010, pp. 121–129.
13.
ÇolakR., AltinokH. and EtM., Generalized difference sequences of fuzzy numbers, Chaos, Solitons & Fractals40 (2009), 1106–1117.
14.
ÇolakR., AltinY and MursaleenM, On some sets of difference sequences of fuzzy numbers, Soft Computing15 (2011), 787–793.
15.
ConnorJ.S., The statistical and strong p-Cesaro convergence of sequences, Analysis8 (1988), 47–63.
16.
EtM., Strongly almost summable difference sequences of order m defined by a modulus, Studia Sci Math Hungar40(4) (2003), 463–476.
17.
EtM., Spaces of Cesáro difference sequences of order r defined by a modulus function in a locally convex space, Taiwanese J Math10(4) (2006), 865–879.
18.
EtM. and ÇolakR., On some generalized difference sequence spaces, Soochow J Math21(4) (1995), 377–386.
19.
FastH., Sur la convergence statistique, Colloq Math2 (1951), 241–244.
20.
FreedmanA.R., SemberJ.J. and RaphaelM., Some Cesaro-type summability spaces, Proc Lond Math Soc37(3) (1978), 508–520.
21.
FridyJ., On statistical convergence, Analysis5 (1985), 301–313.
GadjievA.D. and OrhanC., Some approximation theorems via statistical convergence, Rocky Mountain J Math32(1) (2002), 129–138.
24.
GökhanA., EtM. and MursaleenM., Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers, Math Comput Modelling49(3-4) (2009), 548–555.
25.
KizmazH., On certain sequence spaces, Canad Math Bull24(2) (1981), 169–176.
26.
MursaleenM., λ-statistical convergence, Math Slovaca50(1) (2000), 111–115.
27.
MursaleenM. and MohiuddineS.A., On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, Jour Comput Appl Math233(2) (2009), 142–149.
28.
MatlokaM., Sequences of fuzzy numbers, Busefal28 (1986), 28–37.
29.
NakanoH., Concave modulars, J Math Soc Japan5 (1953), 29–49.
30.
SarmaB., On a class of sequences of fuzzy numbers defined by modulus function, International Journal of Science & Technology2(1) (2007), 25–28.
31.
SchoenbergI.J., The integrability of certain functions and related summability methods, Amer Math Monthly66 (1959), 361–375.
32.
SteinhausH., Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum2 (1951), 73–74.
33.
ŞengülH. and EtM, On lacunary statistical convergence of order α, Acta Mathematica Scientia34B(2) (2014), 473–482.
34.
TaloÖ. and BaşarF., Certain spaces of sequences of fuzzy numbers defined by a modulus function, Demonstratio Math43(1) (2010), 139–149.
35.
TripathyB.C. and BaruahA., Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math Jour50 (2010), 565–574.
36.
ZygmundA., Trigonometric Series, Cambridge University Press, Cambridge, UK, 1979.