Asymptotically ??-Equivalence of Sequences of Sets

In this study, we introduce the concepts of Wijsman asymptotically ?-invariant equivalence (??? ? ), Wijsman asymptotically strongly ?-invariant equivalence ([??? ? ]?) and Wijsman asymptotically ?∗- invariant equivalence (??? ∗ ? ). Also, we investigate the relationships among the concepts of Wijsman asymptotically invariant equivalence, Wijsman asymptotically invariant statistical equivalence, ??? ? , [??? ? ]? and ??? ∗ ? .

___

Ö. Kişi and F. Nuray, “On ?? ? (?)- asymptotically statistical equivalence of sequences of sets,” ISRN Mathematical Analysis, vol. 2013, Article ID 602963, 6 pages, 2013. doi:10.1155/2013/602963

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

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

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

F. Nuray, H. Gök, and U. Ulusu, “?? - convergence,” Math. Commun., vol.16, pp. 531–538, 2011. F. Nuray and B. E. Rhoades, “Statistical convergence of sequences of sets,” Fasc. Math., vol. 49, pp. 87–99, 2012.

N. Pancarogğlu 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.

N. Pancarogğlu, F. Nuray, and E. Savaş, “On asymptotically lacunary invariant statistical equivalent set sequences,” AIP Conf. Proc., vol. 1558, no. 1, pp. 780–781, 2013. doi:10.1063/1.4825609

E. Savaş, “Strongly ?-convergent sequences,” Bull. Calcutta Math., vol. 81, pp. 295–300, 1989.

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

U. Ulusu and F. Nuray, “On asymptotically lacunary statistical equivalent set sequences,” Journal of Mathematics, vol. 2013, Article ID 310438, 5 pages, 2013. doi:10.1155/2013/310438