(f, p)-Asymptotically Lacunary Equivalent Sequences with Respect to the Ideal I

Abstract

In this study, we define (f, p)-Asymptotically Lacunary Equivalent Sequences with respect to the ideal I using a non-trivial ideal , a lacunary sequence , a strictly positive sequence , and a modulus function f, and obtain some revelent connections between these notions.

Share and Cite:

Bilgin, T. (2015) (f, p)-Asymptotically Lacunary Equivalent Sequences with Respect to the Ideal I. Journal of Applied Mathematics and Physics, 3, 1207-1217. doi: 10.4236/jamp.2015.39148.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Freedman, A.R, Sember, J.J. and Raphel, M. (1978) Some Cesaro-Type Summability Spaces. Proceedings London Mathematical Society, 37, 508-520.
http://dx.doi.org/10.1112/plms/s3-37.3.508
[2] Nakano, H. (1953) Concave Modulars. Journal of the Mathematical Society of Japan, 5, 29-49.
http://dx.doi.org/10.2969/jmsj/00510029
[3] Connor, J.S. (1989) On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence. Canadian Mathematical Bulletin, 32, 194-198.
http://dx.doi.org/10.4153/CMB-1989-029-3
[4] Kolk, E. (1993) On Strong Boundedness and Summability with Respect to a Sequence Moduli. Tartu ülikooli Toimetised, 960, 41-50.
[5] Maddox, I.J. (1986) Sequence Spaces Defined by a Modulus. Mathematical Proceedings of the Cambridge Philosophical Society, 100, 161-166.
http://dx.doi.org/10.1017/S0305004100065968
[6] Öztürk, E. and Bilgin, T. (1994) Strongly Summable Sequence Spaces Defined by a Modulus. Indian Journal of Pure and Applied Mathematics, 25, 621-625.
[7] Pehlivan, S. and Fisher, B. (1994) On Some Sequence Spaces. Indian Journal of Pure and Applied Mathematics, 25, 1067-1071.
[8] Ruckle, W.H (1973) FK Spaces in Which the Sequence of Coordinate Vectors Is Bounded. Canadian Journal of Mathematics, 25, 973-978.
http://dx.doi.org/10.4153/CJM-1973-102-9
[9] Marouf, M. (1993) Asymptotic Equivalence and Summability. International Journal of Mathematics and Mathematical Sciences, 16, 755-762.
http://dx.doi.org/10.1155/S0161171293000948
[10] Patterson, R.F. (2003) On Asymptotically Statistically Equivalent Sequences. Demonstratio Mathematica, 36, 149-153.
[11] Metin, B. and Selma, A. (2008) On δ-Lacunary Statistical Asymptotically Equivalent Sequences. Filomat, 22, 161-172.
http://dx.doi.org/10.2298/FIL0801161B
[12] Basarir, M. and Altundag, S. (2011) On Asymptotically Equivalent Difference Sequences with Respect to a Modulus Function. Ricerche di Matematica, 60, 299-311.
http://dx.doi.org/10.1007/s11587-011-0106-0
[13] Patterson, R.F. and Savas, E. (2006) On Asymptotically Lacunary Statistically Equivalent Sequences. Thai Journal of Mathematics, 4, 267-272.
[14] Kostyrko, P., Salat, T. and Wilczynski, W. (2001) I-Convergence. Real Analysis Exchange, 26, 669-686.
[15] Das, P., Savas, E. and Ghosal, S. (2011) On Generalizations of Certain Summability Methods Using Ideals. Applied Mathematics Letters, 24, 1509-1514.
http://dx.doi.org/10.1016/j.aml.2011.03.036
[16] Dems, K. (2004) On I-Cauchy Sequences. Real Analysis Exchange, 30, 123-128.
[17] Savas, E. and Gumus, H. (2013) A Generalization on Ι-Asymptotically Lacunary Statistical Equivalent Sequences. Journal of Inequalities and Applications, 2013, 270.
[18] Kumar, V. and Sharma, A. (2012) Asymptotically Lacunary Equivalent Sequences Defined by Ideals and Modulus Function. Mathematical Sciences, 6, 1-5.
[19] Kumar, V. and Mursaleen, M. (2003) On Ideal Analogue of Asymptotically Lacunary Statistical Equivalence of Sequences. Acta Universitatis Apulensis, 36, 109-119.
[20] Bilgin, T. (2011) f-Asymptotically Lacunary Equivalent Sequences. Acta Universitatis Apulensis, 28, 271-278.
[21] Connor, J.S. (1988) The Statistical and Strong p-Cesaro Convergence of Sequences. Analysis, 8, 47-63.
http://dx.doi.org/10.1524/anly.1988.8.12.47
[22] Fast, H. (1951) Sur la convergence statistique. Colloquium Mathematicae, 2, 241-244.
[23] Fridy, J.A. (1985) On Statistical Convergence. Analysis, 5, 301-313.
http://dx.doi.org/10.1524/anly.1985.5.4.301
[24] Fridy, J.A. and Orhan, C. (1993) Lacunary Statistical Convergent. Pacific Journal of Mathematics, 160, 43-51.
http://dx.doi.org/10.2140/pjm.1993.160.43
[25] Fridy, J.A. and Orhan, C. (1993) Lacunary Statistical Summability. Journal of Mathematical Analysis and Applications, 173, 497-504.
http://dx.doi.org/10.1006/jmaa.1993.1082

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.