In this study, we have investigated the concepts of lacunary summable, lacunary statistical convergence and lacunary statistically Cauchy sequence for double sequences in fuzzy normed spaces. Also, we have investigated some properties and relationships between these concepts.
AltayB. and BaşarF., Some new spaces of double sequences, J Math Anal Appl309(1) (2005), 70–90.
2.
AltinokH., AltinY. and EtM., Lacunary almost statistical convergence of fuzzy numbers, Thai Journal of Mathematics2(2) (2004), 265–274.
3.
AltinokH. and KasapM., f-statistical convergence of order β for sequences of fuzzy numbers, Journal of Intelligent and Fuzzy Systems33 (2016).
4.
BagT. and SamantaS.K., Fixed point theorems in Felbin’s type fuzzy normed linear spaces, J Fuzzy Math16(1) (2008), 243–260.
5.
ÇakanC.
and B.Altay, Statistically boundedness and statistical core of double sequences, J Math Anal Appl317 (2006), 690–697.
6.
DiamondP., KloedenP.Metric Spaces of Fuzzy Sets-Theory and Applications, World Scientific Publishing, Singapore, 1994.
7.
DündarE., UlusuU. and PancaroğluN., Strongly I2-lacunary convergence and I2-lacunary cauchy double sequences of sets, The Aligarh Bulletin of Mathematics35(1-2) (2016), 1–15.
8.
DündarE. and TaloÖ., I2-convergence of double sequences of fuzzy numbers, Iran J Fuzzy Syst (Accepted).
9.
FangJ.-X. and HuangH., On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets Systems147 (2004), 417–435.
10.
FastH., Sur la convergence statistique, Colloq Math2 (1951), 241–244.
11.
FelbinC., Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems48(2) (1992), 239–248.
12.
FridyJ.A., On statistical convergence, Analysis5 (1985), 301–313.
13.
FridyJ.A. and OrhanC., Lacunary statistical convergence, Pasific Journal of Mathematics160(1) (1993), 43–51.
14.
MatlokaM., Sequences of fuzzy numbers, Busefal28 (1986), 28–37.
15.
MizumotoM., TanakaK., Some properties of fuzzy numbers, Advances in Fuzzy Set Theory and ApplicationsNorth-Holland (Amsterdam), 1979, pp. 153–164.
16.
MohiuddineS.A., ŞevliH. and CancanM., Statistical convergence of double sequences in fuzzy normed spaces, Filomat26(4) (2012), 673–681.
17.
MursaleenM. and EdelyO.H.H., Statistical convergence of double sequences, J Math Anal Appl288 (2003), 223–231.
18.
NandaS., On sequences of fuzzy numbers, Fuzzy Sets Systems33 (1989), 123–126.
19.
NurayF., UlusuU. and DündarE., Lacunary statistical convergence of double sequences of sets, Soft Computing20(7) (2016), 2883–2888.
20.
NurayF., Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets Systems99 (1998), 353–355.
21.
NurayF. and SavaşE., Statistical convergence of sequences of fuzzy numbers, Math Slovaca45(3) (1995), 269–273.
22.
PringsheimA., Zur theorie der zweifach unendlichen Zahlenfolgen, Math Ann53 (1900), 289–321.
23.
RathD. and TripatyB.C., On statistically convergence and statistically Cauchy sequences, Indian J Pure Appl Math25(4) (1994), 381–386.
24.
ŠalátT., On statistically convergent sequences of real numbers, Math Slovaca30 (1980), 139–150.
25.
SavaşE., On statistical convergent sequences of fuzzy numbers, Inform Sci137 (2001), 277–282.
26.
SavaşE.
and M.Mursaleen, On statistically convergent double sequences of fuzzy numbers, Inform Sci162 (2004), 183–192.
27.
SavaşE., On I -lacunary statistical convergence of weight g of fuzzy numbers, Journal of Intelligent and Fuzzy Systems32 (2017), 1111–1117.
28.
SavaşE., On lacunary p-summable convergence of weight g for fuzzy numbers via ideal, Journal of Intelligent and Fuzzy Systems34 (2018), 2121–2127.
29.
SchoenbergI.J., The integrability of certain functions and related summability methods, Amer Math Monthly66 (1959), 361–375.
30.
SencimenC.
and S.Pehlivan, Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems159 (2008), 361–370.
31.
SteinhausH., Sur la convergence ordinaire et la convergence asymptotique, Colloq Math2 (1951), 73–74.
32.
TürkmenM.R. and C˙inarM., Lacunary statistical convergence in fuzzy normed linear spaces, Applied and Computational Mathematics6(5) (2017), 233–237.
33.
TürkmenM.R. and C˙inarM., Lambda statistical convergence in fuzzy normed linear spaces, Journal of Intelligent and Fuzzy Systems34(6) (2018), 4023–4030.
34.
TürkmenM.R. and EfeH., On some properties of closability of farthest point maps in fuzzy n-Normed spaces, Imanager’s Journal on Mathematics2(4) (2013), 33–38.
