In this paper, the concept of asymptotically lacunary -invariant equivalence, the concepts of asymptotically lacunary σ2-equivalence and the concept of asymptotically lacunary invariant S2-equivalence for double sequences are defined. In addition, some relationships were obtained among these new equivalence concepts.
HazarikaB. and KumarV., On asymptotically double lacunary statistical equivalent sequences in ideal context, Journal of Inequlities and Applications, 2013(543) (2013), 1–15.
5.
HazarikaB., On asymptotically ideal equivalent sequences, Journal of the Egyptian Mathematical Society23(1) (2015), 67–72.
6.
KostyrkoP., WilczyńskiW. and ŠalátT., I-convergence, Real Anal Exchange26(2) (2000), 669–686.
7.
KostyrkoP., MacajM., ŠalátT. and SleziakM., I-convergence and extermal I-limit points, Math. Slovaca55(4) (2005), 443–464.
8.
KumarV., On I and I*-convergence of double sequences, Math. Commun12(2) (2007), 171–181.
9.
MaroufM., Asymptotic equivalence and summability, Int. J. Math. Math. Sci16(4) (1993), 755–762.
10.
MursaleenM., Invariant means and some matrix transformations, Tamkang J. Math10(2) (1979), 183–188.
11.
MursaleenM., Matrix transformation between some new sequence spaces, Houston J. Math9(4) (1983), 505–509.
12.
MursaleenM. and EdelyO.H.H., Statistical convergence of double sequences, J. Math. Anal. Appl288(1) (2003), 223–231.
13.
MursaleenM. and EdelyO.H.H., On the invariant mean and statistical convergence, Appl. Math. Lett22(11) (2009), 1700–1704.
14.
MursaleenM., MohiuddineS.A. and EdelyO.H.H., On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput. Math. Appl59(2) (2010), 603–611.
15.
MursaleenM. and MohiuddineS.A., On ideal convergence of double sequences in probabilistic normed spaces, Mathematical Reports, 12(62)(4) (2010), 359–371.
16.
MursaleenM. and AlotaibiA., On I-convergence in random 2-normed spaces, Mathematica Slovaca61(6) (2011), 933–940.
17.
NurayF., GökH. and UlusuU., Iσ-convergence, Math Commun16(2) (2011), 531–538.
18.
PancaroğluN. and NurayF., Statistical lacunary invariant summability, Theoretical Mathematics and Applications3(2) (2013), 71–78.
19.
PattersonR.F. and SavaşE., Lacunary statitistical convergence of double sequences, Math. Commun10(1) (2005), 55–61.
20.
PattersonR.F. and SavaşE., On asymptotically lacunary statistically equivalent sequences, Thai J Math4(2) (2006), 267–272.
21.
PringsheimA., Zur theorie der zweifach unendlichen Zahlenfolgen, Math Ann53(3) (1900), 289–321.
22.
RaimiR.A., Invariant means and invariant matrix methods of summability, Duke Math J30(1) (1963), 81–94.
23.
SavaşE., Some sequence spaces involving invariant means, Indian J Math31 (1989), 1–8.
24.
SavaşE., On lacunary strong σ-convergence, Indian J Pure Appl Math21(4) (1990), 359–365.
25.
SavaşE. and NurayF., On σ-statistically convergence and lacunary σ-statistically convergence, Math Slovaca43(3) (1993), 309–315.
26.
SavaşE. and PattersonR.F., σ-asymptotically lacunary statistical equivalent sequences, Open Mathematics4(4) (2006), 648–655.
27.
SavaşE. and PattersonR.F., Double σ-convergence lacunary statistical sequences, Journal of Computational Analysis and Applications11(4) (2009), x–x.
SavaşE., On I-lacunary statistical convergence of weight g of fuzzy numbers, Journal of Intelligent and Fuzzy System32 (2017), 1111–1117.
30.
SchaeferP., Infinite matrices and invariant means, Proc. Amer. Math. Soc36(1) (1972), 104–110.
31.
TürkmenM.R. and DündarE., On lacunary statistical convergence of double sequences and some properties in fuzzy normed spaces, Journal of Intelligent and Fuzzy SystemPrepres (2018), x–x.
UlusuU., DündarE. and NurayF., Lacunary I2-invariant convergence and some properties, International Journal of Analysis and Applications16(3) (2018), 317–327.
34.
U. Ulusu, F. Nuray, Lacunary I -convergence, (under review).
