In the present paper, we introduce the concept of strongly summable with respect to the Orlicz function M and examine the notions statistical convergence and strong summability for different two lacunary sequences and β ∈ (0, 1] . Moreover, we show that a sequence is statistically convergent if it is strongly summable, where θ ={ kr } and θ′ ={ sr } are two lacunary sequences and give some inclusion relations between them.
AltinY., EtM. and TripathyB.C., The sequence space on seminormed spaces, Appl Math Comput154(2) (2004), 423–430.
2.
AkçayF.G. and
AytarS., Rough convergence of a sequence of fuzzy numbers, Bull Math Anal Appl7(4) (2015), 17–23.
3.
AltinokH. and YağdiranD., Lacunary statistical convergence of order β in difference sequences of fuzzy numbers, Journal of Intelligent & Fuzzy Systems31 (2016), 227–235.
4.
AltinokH., AltinY. and IşikM., Statistical convergence and strong p–Cesàro summability of order β in sequences of fuzzy numbers, Iranian J of Fuzzy Systems9(2) (2012), 65–75.
5.
AytarS., The rough limit set and the core of a real sequence, Numer Funct Anal Optim29 (2008), 283–290.
6.
ÇakalliH., On statistical convergence in topological groups, Pure Appl Math Sci43 (1996), 27–31.
7.
CasertaA., MaioG.D. and KočcinacL.D.R., Statistical convergence in function spaces, Abstr Appl Anal (2011), 11. Article ID 420419.
8.
ÇolakR., Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010, pp. 121–129.
9.
ConnorJ.S., The statistical and strong p–Cesaro convergence of sequences, Analysis8 (1988), 47–63.
10.
EtM., Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequences, Appl Math Comput219(17) (2013), 9372–9376.
11.
EtM., ÇinarM. and
KarakaşM., On λ– statistical convergence of order α of sequences of function, J Inequal Appl204 (2013), 8.
12.
EtM. and ŞengülH., Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat28(8) (2014), 1593–1602.
13.
EtM., AltinokH. and AltinY., On some generalized sequence spaces, Appl Math Comput154(1) (2004), 167–173.
14.
FastH., Sur la convergence statistique, Colloq Math2 (1951), 241–244.
15.
FridyJ., On statistical convergence, Analysis5 (1985), 301–313.
16.
FreedmanA.R., SemberJ.J. and RaphaelM., Some Cesaro-type summability spaces, Proc Lond Math Soc37(3) (1978), 508–520.
KawamuraH., TaniA., YamadaM. and TsunodaK., Real time prediction of earthquake ground motions and structural responses by statistic and fuzzy logic, First International Symposium on Uncertainty Modeling and Analysis, Proceedings, USA, 1990, pp. 534–538.
19.
KelavaO. and SeikkalaS., On fuzzy metric spaces, Fuzzy Sets and Systems12(3) (1984), 215–229.
20.
KizmazH., On certain sequence spaces, Canadian Math Bull24 (1981), 169–176.
21.
MatlokaM., Sequences of fuzzy numbers, Busefal28 (1986), 28–37.
22.
MehdiJ.H., ZareH.K., EslamipoorR. and SepehriarA., A developed distance method for ranking generalized fuzzy numbers, Neural Computing and Applications25(3) (2014), 727–731.
23.
MursaleenM., KhanQ.A. and ChishtiT.A., Some new convergent sequences spaces defined by Orlicz functions and statistical convergence, Ital J Pure Appl Math9 (2001), 25–32.
24.
MursaleenM., ÇolakR. and EtM., Some geometric inequalities in a new Banach sequence space, J Inequal Appl (2007), 6. Art. ID 86757.
25.
MursaleenM., SrivastavaH.M. and SharmaS.K., Generalized statistically convergent sequences of fuzzy numbers, Journal of Intelligent & Fuzzy Systems30(3) (2016), 1511–1518.
26.
NurayF. and SavaşE., Statistical convergence of sequences of fuzzy real numbers, Math Slovaca45(3) (1995), 269–273.
27.
QiuD., LuC., ZhangW. and LanY., Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mares equicalence relation, Fuzzy Sets and Systems245 (2014), 63–82.
28.
QiuD. and ZhangW., Symmetric fuzzy numbers and additive equivalence of fuzzy numbers, Soft Computing17 (2013), 1471–1477.
29.
EslamipoorR., NasabH.H. and SepehriarA., An improved ranking method for generalized fuzzy numbers based on Euclidian distance concept, Afr Mat26 (2015), 1291–1297.
30.
ŠalátT., On statistically convergent sequences of real numbers, Math Slovaca30 (1980), 139–150.
31.
SchoenbergI.J., The integrability of certain functions and related summability methods, Amer Math Monthly66 (1959), 361–375.
32.
SavasE. and RhoadesB.E., On some new sequence spaces of invariant means defined by Orlicz functions, Math Inequal Appl5(2) (2002), 271–281.
33.
TripathyB.C. and DuttaH., On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q–lacunary –statistical convergence, An Ştiinţ Univ “Ovidius” Constanţa Ser Mat20(1) (2012), 417–430.
34.
TripathyB.C., SenM. and NathS., I-convergence in probabilistic n–normed space, Soft Comput16 (2012), 1021–1027.
35.
ZhanJ., YuB. and FoteaV.E., Characterizations of two kinds of hemirings based on probability spaces, Soft Computing20 (2016), 637–648.
36.
ZhanJ., LiuQ. and DavvazB., A new rough set theory; rough soft hemirings, Journal of Intelligent & Fuzzy Systems28 (2015), 1687–1697.
