ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES

Abstract

In this paper, we introduce the concept of I2􀀀asymptotically 2􀀀statistically equivalence of multiple L for the double sequences (xkl) and (ykl). Also we give some inclusion relations.

Keywords

• Double Statistical convergence,I2􀀀convergence,2􀀀convergence,asymptotically equivalence,double sequences.

References

1. [1] Esi, A., Acikgoz, M., (2014). On 2􀀀Asymptotically Double Statistical Equiv- alent Sequences, Int. J. Nonlinear Anal. Appl. 5. No. 2, 16-21 ISNN:2008-6822.
2. [2] Fast, H. (1951). Sur la convergence statistique, Coll. Math., 2, 241-244.
3. [3] Freedman, A. R. and Sember, J. J. (1981) Densities and Summability, Pacic Journal of Mathematics, 95, 239- 305.
4. [4] Fridy, J. A. (1985). On statistical convergence. Analysis, 5, 301, 313.
5. [5] Gumus, H., Savas, E. (2012) On SL asymptotically statistical equivalent sequences, Numerical Analysis and Applied Mathematics Icnaam Ap Conf. Proc. 1479, pp.936-941
6. [6] Hazarika, B., Kumar V., (2013), On asymptotically double lacunary statistical equivalent sequences in ideal context, J. Ineq. Appl. 2013:543
7. [7] Kostyrko P. , Salat T. , Wilczynski W., I􀀀convergence, Real Anal. Exchange, 26 (2) (2000/2001), 669-686.
8. [8] Kostyrko P. , Macaj M. , Salat T. , and Sleziak M. , \I􀀀convergence and extremal I􀀀limit points,"Mathematica Slovaca, vol. 55, no. 4, pp. 443{464, 2005.

9. [9] Marouf, M. (1993) Asymptotic equivalence and summability. Internat. J. Math. Sci., 16 (4)
10. [10] Mursaleen, (2000), 􀀀Statistical Convergence, Math. Slovaca, 50, No. 1, pp. 111-115.
11. [11] Mursaleen M., Edely O.H.H. (2003), Statistical convergence of double se- quences, J. Math. Anal. Appl., 288,223-231.
12. [12] Patterson, R.F. (2003). On asymptotically statistically equivalent sequences. Demostratio Math., (1), 149-153.
13. [13] Patterson, R.F. Some characterization of asymptotic equivalent double se- quences, (in press).
14. [14] Pobyvanets I. P. (1980). Asymptotic equivalence of some linear transforma- tions, dened by a nonnegative matrix and reduced to generalized equivalence in the sense of Cesaro and Abel. Mat. Fiz., no. 28, 83{87, 123. MR 632482 (83h:40004).
15. [15] Pringsheim A. (1900). Zur theorie der zweifach unendlichen Zahlenfolgen, Mathematische Annalen 53 289-321
16. [16] Savas, E., Das P. (2011). A generalized statistical convergence via ideals. Appl.Math. Lett., 24 826{830.
17. [17] Savas, E. (2012). On generalized double statistical convergence via ideals. The Fifth Saudi Science Conference. 16-18 April, 2012.
18. [18] Savas, R., Basarr M., (2006). (; )-Asymptotically Statistically Equivalent Sequences, Filomat 20 (1), 35-42.
19. [19] Schoenberg, I. J., (1959). The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, 361-375.