___

H. Fast, “Sur la convergence statistique,” Colloq. Math., vol. 2, pp. 241-244, 1951.

I. J. Schoenberg, “The integrability of certain functions and related summability methods,” Amer. Math. Monthly, vol. 66, pp. 361-375, 1959.

J. A. Fridy, and C. Orhan, “Lacunary statistical convergence,” Pacific J. Math., vol. 160, no. 1, pp. 43-51, 1993.

P. Kostyrko, T. Šalát, and W. Wilczyński, “ℐ- Convergence,” Real Anal. Exchange, vol. 26, no. 2, pp. 669-686, 2000.

P. Das, E. Savaş and S. Kr. Ghosal, “On generalizations of certain summability methods using ideals,” Appl. Math. Lett., vol. 24, no. 9, pp. 1509-1514, 2011.

F. Nuray, and B. E. Rhoades, “Statistical convergence of sequences of sets,” Fasc. Math., vol. 49, pp. 87-99, 2012.

U. Ulusu, and F. Nuray, “Lacunary statistical convergence of sequence of sets,” Progress in Applied Mathematics, vol. 4, no. 2, pp. 99-109, 2012.

Ö. Kişi, and F. Nuray, “A new convergence for sequences of sets, Abstract and Applied Analysis, Article ID 852796, 6 pages, 2013.

U. Ulusu, and E. Dündar, “ℐ-Lacunary Statistical Convergence of Sequences of Sets,” Filomat, vol. 28, no. 8, pp. 1567-1574, 2013.

R. A. Raimi, “Invariant means and invariant matrix methods of summability,” Duke Math. J., vol. 30 , pp. 81-94, 1963. P. Schaefer, “Infinite matrices and invariant means,” Proc. Amer. Math. Soc., vol. 36, pp. 104-110, 1972.

M. Mursaleen, “Invariant means and some matrix transformations,” Tamkang J. Math., vol. 10, no. 2, pp. 183-188, 1979.

M. Mursaleen, “Matrix transformation between some new sequence spaces,” Houston J. Math., vol. 9 , no. 4, pp. 505-509, 1983.

E. Savaş, “Some sequence spaces involving invariant means,” Indian J. Math., vol. 31, pp. 1- 8, 1989.

E. Savaş, “Strong σ-convergent sequences,” Bull. Calcutta Math., vol. 81, pp. 295-300, 1989.

M. Mursaleen, and O. H. H. Edely, “On the invariant mean and statistical convergence,” Appl. Math. Lett., vol. 22, no. 11, pp. 1700-1704, 2009.

N. Pancaroğlu, and F. Nuray, “Statistical lacunary invariant summability,” Theoretical Mathematics and Applications, vol. 3, no. 2, pp. 71-78, 2013.

N. Pancaroğlu, and F. Nuray, “On Invariant Statistically Convergence and Lacunary Invariant Statistically Convergence of Sequences of Sets,” Progress in Applied Mathematics, vol. 5, no. 2, pp. 23-29, 2013.

E. Savaş, and F. Nuray, “On σ-statistically convergence and lacunary σ-statistically convergence,” Math. Slovaca, vol. 43, no. 3, 309-315, 1993.

U. Ulusu, and F. Nuray, “Lacunary ℐ- convergence,” (under review).

M. Marouf, “Asymptotic equivalence and summability,” Int. J. Math. Math. Sci., vol. 16, no. 4, pp. 755-762, 1993.

R. F. Patterson, and E. Savaş,” On asymptotically lacunary statistically equivalent sequences,” Thai J. Math., vol. 4, no. 2, pp. 267- 272, 2006.

E. Savaş, and R. F. Patterson, “σ-asymptotically lacunary statistical equivalent sequences,” Central European Journal of Mathematics, vol. 4, no. 4, pp. 648-655, 2006.

U. Ulusu, and F. Nuray, “On asymptotically lacunary statistical equivalent set sequences,” Journal of Mathematics, Article ID 310438, 5 pages, 2013.

N. Pancaroğlu, F. Nuray, and E. Savaş, “On asymptotically lacunary invariant statistical equivalent set sequence,” AIP Conf. Proc., 1558:780, 2013.

U. Ulusu, and E. Gülle, “Asymptotically “ℐ- equivalence of sequences of sets,” (under review).

H. Nakano, “Concave modulars,” J. Math. Soc. Japan, vol. 5, pp. 29-49, 1953.

I. J. Maddox, “Sequence spaces defined by a modulus,” Math. Proc. Camb. Phil. Soc., vol. 100, pp. 161-166, 1986.

S. Pehlivan, and B. Fisher, “Some sequences spaces defined by a modulus,” Mathematica Slovaca, vol. 45, pp. 275-280, 1995.

N. Pancaroğlu, and F. Nuray, “Invariant Statistical Convergence of Sequences of Sets with respect to a Modulus Function,” Abstract and Applied Analysis, Article ID 818020, 5 pages, 2014.

N. Pancaroğlu, and F. Nuray, “Lacunary Invariant Statistical Convergence of Sequences of Sets with respect to a Modulus Function,” Journal of Mathematics and System Science, vol. 5, pp. 122-126, 2015.

V. Kumar, and A. Sharma, “Asymptotically lacunary equivalent sequences defined by ideals and modulus function,” Mathematical Sciences, vol. 6, no. 23, 5 pages, 2012.

Ö. Kişi, H. Gümüş, and F. Nuray, “ℐ- Asymptotically lacunary equivalent set sequences defined by modulus function,” Acta Universitatis Apulensis, vol. 41, pp. 141-151, 2015.

N. P. Akın, and E. Dündar, “Asymptotically ℐ- Invariant Statistical Equivalence of Sequences of Set Defined By A Modulus Function,” (under review).

R. A. Wijsman, “Convergence of sequences of convex sets, cones and functions,” Bull. Amer. Math. Soc., vol. 70, pp. 186-188, 1964.

G. Beer, “On convergence of closed sets in a metric space and distance functions,” Bull. Aust. Math. Soc., vol. 31, pp. 421-432, 1985.

M. Baronti, and P. Papini, “Convergence of sequences of sets,” In Methods of Functional Analysis in Approximation Theory, ISNM 76, Birkhäuser, Basel, pp. 133-155, 1986.

F. Nuray, H. Gök, and U. Ulusu, ℐ- convergence, Math. Commun., vol. 16, pp. 531- 538, 2011.

E. E. Kara, and M. İlkhan, “On some paranormed A-ideal convergent sequence spaces defined by Orlicz function,” Asian J. Math. Comput. Research, vol. 4, no. 4, pp. 183-194, 2015.

E. E. Kara, and M. İlkhan, “Lacunary ℐ- convergent and lacunary ℐ-bounded sequence spaces define by an Orlicz function,” Electron. J. Math. Anal. Appl., vol. 4, no. 2, pp. 87-94, 2016.

E. E. Kara, M. Dastan, and M İlkhan, “On lacunary ideal convergence of some sequence,” New Trends in Mathematical Science, vol. 5, no. 1, pp. 234-242, 2017.

U. Ulusu, and E. Dündar, “Asymptottically ℐ- Cesaro equivalence of sequences of sets,” Universal Journal of Mathematics and Applications, vol. 1, no. 2, pp. 101-1015, 2018.