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

Ömer Kişi

Research Article

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

Year 2015, Volume: 3 Issue: 2, 165 - 175, 01.10.2015

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] 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] Fast, H. (1951). Sur la convergence statistique, Coll. Math., 2, 241-244.
[3] Freedman, A. R. and Sember, J. J. (1981) Densities and Summability, Pacic Journal of Mathematics, 95, 239- 305.
[4] Fridy, J. A. (1985). On statistical convergence. Analysis, 5, 301, 313.
[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] Hazarika, B., Kumar V., (2013), On asymptotically double lacunary statistical equivalent sequences in ideal context, J. Ineq. Appl. 2013:543
[7] Kostyrko P. , Salat T. , Wilczynski W., I􀀀convergence, Real Anal. Exchange, 26 (2) (2000/2001), 669-686.
[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] Marouf, M. (1993) Asymptotic equivalence and summability. Internat. J. Math. Sci., 16 (4)
[10] Mursaleen, (2000), 􀀀Statistical Convergence, Math. Slovaca, 50, No. 1, pp. 111-115.
[11] Mursaleen M., Edely O.H.H. (2003), Statistical convergence of double se- quences, J. Math. Anal. Appl., 288,223-231.
[12] Patterson, R.F. (2003). On asymptotically statistically equivalent sequences. Demostratio Math., (1), 149-153.
[13] Patterson, R.F. Some characterization of asymptotic equivalent double se- quences, (in press).
[14] Pobyvanets I. P. (1980). Asymptotic equivalence of some linear transforma- tions, dened 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] Pringsheim A. (1900). Zur theorie der zweifach unendlichen Zahlenfolgen, Mathematische Annalen 53 289-321
[16] Savas, E., Das P. (2011). A generalized statistical convergence via ideals. Appl.Math. Lett., 24 826{830.
[17] Savas, E. (2012). On generalized double statistical convergence via ideals. The Fifth Saudi Science Conference. 16-18 April, 2012.
[18] Savas, R., Basarr M., (2006). (; )-Asymptotically Statistically Equivalent Sequences, Filomat 20 (1), 35-42.
[19] Schoenberg, I. J., (1959). The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, 361-375.

Year 2015, Volume: 3 Issue: 2, 165 - 175, 01.10.2015

Ömer Kişi

Abstract

References

[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] Fast, H. (1951). Sur la convergence statistique, Coll. Math., 2, 241-244.
[3] Freedman, A. R. and Sember, J. J. (1981) Densities and Summability, Pacic Journal of Mathematics, 95, 239- 305.
[4] Fridy, J. A. (1985). On statistical convergence. Analysis, 5, 301, 313.
[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] Hazarika, B., Kumar V., (2013), On asymptotically double lacunary statistical equivalent sequences in ideal context, J. Ineq. Appl. 2013:543
[7] Kostyrko P. , Salat T. , Wilczynski W., I􀀀convergence, Real Anal. Exchange, 26 (2) (2000/2001), 669-686.
[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] Marouf, M. (1993) Asymptotic equivalence and summability. Internat. J. Math. Sci., 16 (4)
[10] Mursaleen, (2000), 􀀀Statistical Convergence, Math. Slovaca, 50, No. 1, pp. 111-115.
[11] Mursaleen M., Edely O.H.H. (2003), Statistical convergence of double se- quences, J. Math. Anal. Appl., 288,223-231.
[12] Patterson, R.F. (2003). On asymptotically statistically equivalent sequences. Demostratio Math., (1), 149-153.
[13] Patterson, R.F. Some characterization of asymptotic equivalent double se- quences, (in press).
[14] Pobyvanets I. P. (1980). Asymptotic equivalence of some linear transforma- tions, dened 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] Pringsheim A. (1900). Zur theorie der zweifach unendlichen Zahlenfolgen, Mathematische Annalen 53 289-321
[16] Savas, E., Das P. (2011). A generalized statistical convergence via ideals. Appl.Math. Lett., 24 826{830.
[17] Savas, E. (2012). On generalized double statistical convergence via ideals. The Fifth Saudi Science Conference. 16-18 April, 2012.
[18] Savas, R., Basarr M., (2006). (; )-Asymptotically Statistically Equivalent Sequences, Filomat 20 (1), 35-42.
[19] Schoenberg, I. J., (1959). The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66, 361-375.

There are 19 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Research Article
Authors	Ömer Kişi
Submission Date	July 10, 2014
Publication Date	October 1, 2015
Published in Issue	Year 2015 Volume: 3 Issue: 2

Cite

APA	Kişi, Ö. (2015). ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES. Konuralp Journal of Mathematics, 3(2), 165-175.
AMA	Kişi Ö. ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES. Konuralp J. Math. October 2015;3(2):165-175.
Chicago	Kişi, Ömer. “ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES”. Konuralp Journal of Mathematics 3, no. 2 (October 2015): 165-75.
EndNote	Kişi Ö (October 1, 2015) ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES. Konuralp Journal of Mathematics 3 2 165–175.
IEEE	Ö. Kişi, “ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES”, Konuralp J. Math., vol. 3, no. 2, pp. 165–175, 2015.
ISNAD	Kişi, Ömer. “ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES”. Konuralp Journal of Mathematics 3/2 (October2015), 165-175.
JAMA	Kişi Ö. ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES. Konuralp J. Math. 2015;3:165–175.
MLA	Kişi, Ömer. “ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES”. Konuralp Journal of Mathematics, vol. 3, no. 2, 2015, pp. 165-7.
Vancouver	Kişi Ö. ON I2-ASYMPTOTICALLY $\lambda^2$-STATISTICAL EQUIVALENT DOUBLE SEQUENCES. Konuralp J. Math. 2015;3(2):165-7.