In this paper, we show under which conditions the limit of the distance between nth term of a sequence of fuzzy numbers and nth term of its Cesàro mean of order one tends to zero. As corollaries we prove several Tauberian theorems for Cesàro summability of sequences of fuzzy numbers.
AlotaibiA., MursaleenM., SharmaS.K. and MohiuddineS.A., Sequence spaces of fuzzy numbers defined by a Musielak-Orlicz function, Filomat29(7) (2015), 1461–1468.
2.
AltinY., MursaleenM. and AltinokH., Statistical summability (C, 1) for sequences of fuzzy real numbers and a Tauberian theorem, J Intell Fuzzy Syst21(6) (2010), 379–384.
3.
AltinokH. and MursaleenM., Δ-statistically boundedness for sequences of fuzzy numbers, Taiwanese J Math15(5) (2011), 2081–2093.
4.
BedeB. and GalS.G., Almost periodic fuzzy-number-valued functions, Fuzzy Sets Syst147(3) (2004), 385–403.
5.
Çanakİ., Tauberian theorems for Cesàro summability of sequences of fuzzy numbers, J Intell Fuzzy Systems27(2) (2014), 937–942.
6.
Çanakİ., Hölder summability method of fuzzy numbers and a Tauberian theorem, Iran J Fuzzy Syst11(4) (2014), 87–93.
7.
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.
8.
Çanakİ., On the Riesz mean of sequences of fuzzy real numbers, J Intell Fuzzy Systems26(6) (2014), 2685–2688.
9.
ÇolakR., AltinY. and MursaleenM., On some sets of difference sequences of fuzzy numbers, Soft Comput15 (2011), 787–793.
10.
DikF., Tauberian theorems for convergence and subsequential convergence with controlled oscillatory behavior, Math Morav5 (2001), 19–56.
11.
DikM., Tauberian theorems for sequences with moderately oscillatory control modulo, Math Morav5 (2001), 57–94.
12.
HardyG.H., Divergent series, Oxford University Press,
1949.
13.
ÖnderZ., SezerS.A. and Çanakİ., A Tauberian theorem for the weighted mean method of summability of sequences of fuzzy numbers, J Intell Fuzzy Systems28(3) (2015), 1403–1409.
14.
SchmidtR., Über divergente Folgen und lineare Mittelbildungen, Math Z22 (1925), 89–152.
15.
StanojevićČ.V.,
Analysis of Divergence: Control and Management of Divergent Process, edited by İ Çanak, Graduate
Research Seminar Lecture Notes, University of Missouri-Rolla, Rolla, MO, USA, 1998.
16.
SubrahmanyamP.V., Cesàro summability of fuzzy real numbers, J Anal7 (1999), 159–168.
17.
TaloÖ. and BaşarF., On the slowly decreasing sequences of fuzzy numbers, Abstr Appl Anal2013 (2013), 1–7. Article ID 891986.
18.
TaloÖ. and ÇakanC., On the Cesàro convergence of sequences of fuzzy numbers, Appl Math Lett25 (2012), 676–681.