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Year 2016, Volume: 4 Issue: 2, 91 - 101, 30.10.2016

Ugur Ulusu , Fatih Nuray , Ekrem Savaş

https://doi.org/10.36753/mathenot.421461
Cited By: 2

Abstract

References

  • [1] Aubin, J.-P. and Frankowska, H., Set-valued analysis. Birkhauser, Boston, 1990.
  • [2] Baronti, M. and Papini, P., Convergence of sequences of sets. In methods of functional analysis in approximation theory, ISNM 76, Birkhauser, Basel, 1986.
  • [3] Beer, G., On convergence of closed sets in a metric space and distance functions. Bull. Aust. Math. Soc. 31 (1985), 421-432.
  • [4] Beer, G., Wijsman convergence: A survey. Set-Valued Analysis 2 (1994), 77-94.
  • [5] Connor, J. S., The statistical and strong p-Cesàro convergence of sequences. Analysis 8 (1988), 47-63.
  • [6] Das, P., Sava¸s, E. and Ghosal, S. Kr., On generalizations of certain summability methods using ideals. Appl. Math. Lett. 24 (2011), no. 9, 1509-1514.
  • [7] Fast, H., Sur la convergence statistique. Colloq. Math. 2 (1951), 241-244.
  • [8] Freedman, A. R., Sember, J. J. and Raphael, M., Some Cesaro-type summability spaces. Proc. Lond. Math. Soc. 37 (1978), no. 3, 508-520.
  • [9] Fridy, J. A., On statistical convergence. Analysis 5 (1985), 301-313.
  • [10] Fridy, J. A. and Orhan, C., Lacunary Statistical Convergence. Pacific J. Math. 160 (1993), no. 1, 43-51.
  • [11] Hazarika, B. and Esi, A., Statistically almost λ-convergence of sequences of sets. Eur. J. Pure Appl. Math. 6 (2013), no. 2, 137-146.
  • [12] Hazarika, B. and Esi, A., On λ-asymptotically Wijsman generalized statistical convergence of sequences of sets. Tatra Mt. Math. Publ. 56 (2013), 67-77.
  • [13] Kişi, Ö. and Nuray, F., A new convergence for sequences of sets. Abstr. Appl. Anal. 2013 (2013), Article ID 852796, 6 pages. doi:10.1155/2013/852796.
  • [14] Kişi, Ö. and Nuray, F., On S_λ^L (I)-asymptotically statistical equivalence of sequences of sets. Mathematical Analysis 2013 (2013), Article ID 602963, 6 pages. doi:10.1155/2013/602963.
  • [15] Kişi, Ö., Savaş, E. and Nuray, F., On asymptotically I-lacunary statistical equivalence of sequences of sets. (submitted for publication).
  • [16] Kostyrko, P., Šalát, T. and Wilezynski, W., I-Convergence. Real Anal. Exchange 26 (2000), no. 2, 669-686.
  • [17] Marouf, M., Asymptotic equivalence and summability. Int. J. Math. Math. Sci. 16 (1993), no. 4, 755-762.
  • [18] Nuray, F. and Rhoades, B. E., Statistical convergence of sequences of sets. Fasc. Math. 49 (2012), 87-99.
  • [19] Patterson, R.F., On asymptotically statistically equivalent sequences. Demostratio Mathematica 36 (2003), no. 1, 149-153.
  • [20] Patterson, R.F. and Sava¸s, E., On asymptotically lacunary statistically equivalent sequences. Thai J. Math. 4 (2006), no. 2, 267-272.
  • [21] Sava¸s, E. and Patterson, R.F., An extension asymptotically lacunary statistically equivalent sequences. Aligarh Bull. Math. 27 (2008), no. 2, 109-113.
  • [22] Sava¸s, E. and Das, P., A generalized statistical convergence via ideals. Appl. Math. Lett. 24 (2011), no. 6, 826-830. [23] Sava¸s, E., On I-asymptotically lacunary statistical equivalent sequences. Adv. Difference Equ. 111 (2013), 7 pages. doi:10.1186/1687-1847-2013-111.
  • [24] Sava¸s, E. and Gümü¸s, H., A generalization on I-asymptotically lacunary statistical equivalent sequences. J. Inequal. Appl. 270 (2013), 9 pages. doi: 10.1186/1029-242X-2013-270.
  • [25] Ulusu, U., Asymptotically I-Cesàro equivalence of sequences of sets. (submitted for publication).
  • [26] Ulusu, U. and Kişi, Ö., I-Cesàro summability of sequences of sets. (submitted for publication).
  • [27] Ulusu, U. and Nuray, F., Lacunary statistical convergence of sequence of sets. Progress in Applied Mathematics 4 (2012), no. 2, 99-109.
  • [28] Ulusu, U. and Nuray, F., On asymptotically lacunary statistical equivalent set sequences. Journal of Mathematics 2013 (2013), Article ID 310438, 5 pages. doi: 10.1155/2013/310438.
  • [29] Ulusu, U. and Savaş, E., An extension asymptotically lacunary statistical equivalent set sequences. J. Inequal. Appl. 134 (2014), 8 pages. doi: 10.1186/1029-242X-2014-134.
  • [30] Ulusu, U. and Dündar, E., I-lacunary statistical convergence of sequences of sets. Filomat 28 (2014), no. 8, 1567-1574.
  • [31] Wijsman, R. A., Convergence of sequences of convex sets, cones and functions. Bull. Amer. Math. Soc. 70 (1964), no. 1, 186-188.
  • [32] Wijsman, R. A., Convergence of Sequences of Convex sets, Cones and Functions II. Trans. Amer. Math. Soc. 123 (1966), no. 1, 32-45.

A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets

Year 2016, Volume: 4 Issue: 2, 91 - 101, 30.10.2016

Ugur Ulusu , Fatih Nuray , Ekrem Savaş

https://doi.org/10.36753/mathenot.421461
Cited By: 2

Abstract


Keywords

Asymptotically equivalence statistical convergence I-convergence lacunary sequence Cesàro summability sequences of sets Wijsman convergence

References

  • [1] Aubin, J.-P. and Frankowska, H., Set-valued analysis. Birkhauser, Boston, 1990.
  • [2] Baronti, M. and Papini, P., Convergence of sequences of sets. In methods of functional analysis in approximation theory, ISNM 76, Birkhauser, Basel, 1986.
  • [3] Beer, G., On convergence of closed sets in a metric space and distance functions. Bull. Aust. Math. Soc. 31 (1985), 421-432.
  • [4] Beer, G., Wijsman convergence: A survey. Set-Valued Analysis 2 (1994), 77-94.
  • [5] Connor, J. S., The statistical and strong p-Cesàro convergence of sequences. Analysis 8 (1988), 47-63.
  • [6] Das, P., Sava¸s, E. and Ghosal, S. Kr., On generalizations of certain summability methods using ideals. Appl. Math. Lett. 24 (2011), no. 9, 1509-1514.
  • [7] Fast, H., Sur la convergence statistique. Colloq. Math. 2 (1951), 241-244.
  • [8] Freedman, A. R., Sember, J. J. and Raphael, M., Some Cesaro-type summability spaces. Proc. Lond. Math. Soc. 37 (1978), no. 3, 508-520.
  • [9] Fridy, J. A., On statistical convergence. Analysis 5 (1985), 301-313.
  • [10] Fridy, J. A. and Orhan, C., Lacunary Statistical Convergence. Pacific J. Math. 160 (1993), no. 1, 43-51.
  • [11] Hazarika, B. and Esi, A., Statistically almost λ-convergence of sequences of sets. Eur. J. Pure Appl. Math. 6 (2013), no. 2, 137-146.
  • [12] Hazarika, B. and Esi, A., On λ-asymptotically Wijsman generalized statistical convergence of sequences of sets. Tatra Mt. Math. Publ. 56 (2013), 67-77.
  • [13] Kişi, Ö. and Nuray, F., A new convergence for sequences of sets. Abstr. Appl. Anal. 2013 (2013), Article ID 852796, 6 pages. doi:10.1155/2013/852796.
  • [14] Kişi, Ö. and Nuray, F., On S_λ^L (I)-asymptotically statistical equivalence of sequences of sets. Mathematical Analysis 2013 (2013), Article ID 602963, 6 pages. doi:10.1155/2013/602963.
  • [15] Kişi, Ö., Savaş, E. and Nuray, F., On asymptotically I-lacunary statistical equivalence of sequences of sets. (submitted for publication).
  • [16] Kostyrko, P., Šalát, T. and Wilezynski, W., I-Convergence. Real Anal. Exchange 26 (2000), no. 2, 669-686.
  • [17] Marouf, M., Asymptotic equivalence and summability. Int. J. Math. Math. Sci. 16 (1993), no. 4, 755-762.
  • [18] Nuray, F. and Rhoades, B. E., Statistical convergence of sequences of sets. Fasc. Math. 49 (2012), 87-99.
  • [19] Patterson, R.F., On asymptotically statistically equivalent sequences. Demostratio Mathematica 36 (2003), no. 1, 149-153.
  • [20] Patterson, R.F. and Sava¸s, E., On asymptotically lacunary statistically equivalent sequences. Thai J. Math. 4 (2006), no. 2, 267-272.
  • [21] Sava¸s, E. and Patterson, R.F., An extension asymptotically lacunary statistically equivalent sequences. Aligarh Bull. Math. 27 (2008), no. 2, 109-113.
  • [22] Sava¸s, E. and Das, P., A generalized statistical convergence via ideals. Appl. Math. Lett. 24 (2011), no. 6, 826-830. [23] Sava¸s, E., On I-asymptotically lacunary statistical equivalent sequences. Adv. Difference Equ. 111 (2013), 7 pages. doi:10.1186/1687-1847-2013-111.
  • [24] Sava¸s, E. and Gümü¸s, H., A generalization on I-asymptotically lacunary statistical equivalent sequences. J. Inequal. Appl. 270 (2013), 9 pages. doi: 10.1186/1029-242X-2013-270.
  • [25] Ulusu, U., Asymptotically I-Cesàro equivalence of sequences of sets. (submitted for publication).
  • [26] Ulusu, U. and Kişi, Ö., I-Cesàro summability of sequences of sets. (submitted for publication).
  • [27] Ulusu, U. and Nuray, F., Lacunary statistical convergence of sequence of sets. Progress in Applied Mathematics 4 (2012), no. 2, 99-109.
  • [28] Ulusu, U. and Nuray, F., On asymptotically lacunary statistical equivalent set sequences. Journal of Mathematics 2013 (2013), Article ID 310438, 5 pages. doi: 10.1155/2013/310438.
  • [29] Ulusu, U. and Savaş, E., An extension asymptotically lacunary statistical equivalent set sequences. J. Inequal. Appl. 134 (2014), 8 pages. doi: 10.1186/1029-242X-2014-134.
  • [30] Ulusu, U. and Dündar, E., I-lacunary statistical convergence of sequences of sets. Filomat 28 (2014), no. 8, 1567-1574.
  • [31] Wijsman, R. A., Convergence of sequences of convex sets, cones and functions. Bull. Amer. Math. Soc. 70 (1964), no. 1, 186-188.
  • [32] Wijsman, R. A., Convergence of Sequences of Convex sets, Cones and Functions II. Trans. Amer. Math. Soc. 123 (1966), no. 1, 32-45.
There are 31 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ugur Ulusu

Fatih Nuray

Ekrem Savaş

Publication Date October 30, 2016
Submission Date March 21, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Ulusu, U., Nuray, F., & Savaş, E. (2016). A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets. Mathematical Sciences and Applications E-Notes, 4(2), 91-101. https://doi.org/10.36753/mathenot.421461
AMA Ulusu U, Nuray F, Savaş E. A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets. Math. Sci. Appl. E-Notes. October 2016;4(2):91-101. doi:10.36753/mathenot.421461
Chicago Ulusu, Ugur, Fatih Nuray, and Ekrem Savaş. “A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets”. Mathematical Sciences and Applications E-Notes 4, no. 2 (October 2016): 91-101. https://doi.org/10.36753/mathenot.421461.
EndNote Ulusu U, Nuray F, Savaş E (October 1, 2016) A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets. Mathematical Sciences and Applications E-Notes 4 2 91–101.
IEEE U. Ulusu, F. Nuray, and E. Savaş, “A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 91–101, 2016, doi: 10.36753/mathenot.421461.
ISNAD Ulusu, Ugur et al. “A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets”. Mathematical Sciences and Applications E-Notes 4/2 (October 2016), 91-101. https://doi.org/10.36753/mathenot.421461.
JAMA Ulusu U, Nuray F, Savaş E. A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets. Math. Sci. Appl. E-Notes. 2016;4:91–101.
MLA Ulusu, Ugur et al. “A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, 2016, pp. 91-101, doi:10.36753/mathenot.421461.
Vancouver Ulusu U, Nuray F, Savaş E. A Generalization of Asymptotically I-Lacunary Statistical Equivalence of Sequences of Sets. Math. Sci. Appl. E-Notes. 2016;4(2):91-101.

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