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Year 2017, Volume: 5 Issue: 1, 1 - 10, 01.04.2017

ERDİNÇ Dündar UĞUR Ulusu BÜNYAMİN Aydın

Abstract

References

  • [1] J.-P. Aubin, H. Frankowska, Set-valued analysis, Birkhauser, Boston (1990).
  • [2] M. Baronti, P. Papini, Convergence of sequences of sets, In methods of functional analysis in approximation theory, ISNM 76, Birkhauser, Basel (1986).
  • [3] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421-432.
  • [4] G. Beer, Wijsman convergence: A survey, Set-Valued Anal. 2 (1994), 77-94.
  • [5] P. Das, E. Savas, S. Kr. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Lett. 24(9) (2011), 1509-1514.
  • [6] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620.
  • [7] E. Dundar, B. Altay, I2-convergence and I2-Cauchy double sequences, Acta Mathematica Scientia 34B(2) (2014), 343-353.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [9] J. A. Fridy, C. Orhan, Lacunary statistical convergence, Paci c J. Math. 160(1) (1993), 43-51.
  • [10]  O. Kisi, F. Nuray, New convergence de nitions for sequences of sets, Abstr. Appl. Anal. 2013 (2013), Article ID 852796, 6 pages. doi:10.1155/2013/852796.
  • [11] P. Kostyrko, T. Salat, W. Wilczynski, I-Convergence, Real Anal. Exchange 26(2) (2000), 669-686.
  • [12] M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288(1) (2003), 223-231.
  • [13] F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 8799.
  • [14] F. Nuray, W. H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513-527.
  • [15] F. Nuray, E. Dundar, U. Ulusu, Wijsman I2-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters, 2 (2014), 35-39.
  • [16] F. Nuray, E. Dundar, U. Ulusu, Wijsman statistical convergence of double sequences of sets, (under communication).
  • [17] F. Nuray, U. Ulusu, E. Dundar, Cesaro summability of double sequences of sets, Gen. Math. Notes 25(1) (2014), 8-18.
  • [18] F. Nuray, U. Ulusu, E. Dundar, Lacunary statistical convergence of double sequences of sets, Soft Computing 20(7) (2016), 2883-2888. doi:10.1007/s00500-015-1691-8.
  • [19] E. Savas, P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24(6) (2011), 826-830.
  • [20] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66(5) (1959), 361-375.
  • 21] Y. Sever,  O. Talo, On Statistical Convergence of Double Sequences of Closed Sets, Filomat 30(3) (2016), 533-539. doi:10.2298/FIL1603533S.
  • [22] Y. Sever,  O. Talo, B. Altay, On convergence of double sequences of closed sets, Contemporary Analysis and Applied M athematics 3(1) (2015), 30-49.
  • [23]  O. Talo, Y. Sever, F. Basar, On statistically convergent sequences of closed set, Filomat, 30(6) (2016), 1497-1509. doi:10.2298/FIL1606497T.
  • [24] U. Ulusu, E. Dundar, I-Lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567-1574.
  • [25] U. Ulusu, F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics 4(2) (2012), 99-109.
  • [26] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70(1) (1964), 186-188.
  • [27] R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions II, Trans. Amer. Math. Soc. 123(1) (1966), 32-45.

$I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS

Year 2017, Volume: 5 Issue: 1, 1 - 10, 01.04.2017

ERDİNÇ Dündar UĞUR Ulusu BÜNYAMİN Aydın

Abstract

In this paper, we introduce the concepts of the Wijsman $I_2$- statistical convergence, Wijsman $I_2$-lacunary statistical convergence and Wijsman strongly $I_2$-lacunary convergence of double sequences of sets and investigate the relationship between them.

Keywords

Statistical convergence lacunary sequence I2-convergence double sequence of sets Wijsman convergence

References

  • [1] J.-P. Aubin, H. Frankowska, Set-valued analysis, Birkhauser, Boston (1990).
  • [2] M. Baronti, P. Papini, Convergence of sequences of sets, In methods of functional analysis in approximation theory, ISNM 76, Birkhauser, Basel (1986).
  • [3] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc. 31 (1985), 421-432.
  • [4] G. Beer, Wijsman convergence: A survey, Set-Valued Anal. 2 (1994), 77-94.
  • [5] P. Das, E. Savas, S. Kr. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Lett. 24(9) (2011), 1509-1514.
  • [6] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, I and I-convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620.
  • [7] E. Dundar, B. Altay, I2-convergence and I2-Cauchy double sequences, Acta Mathematica Scientia 34B(2) (2014), 343-353.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [9] J. A. Fridy, C. Orhan, Lacunary statistical convergence, Paci c J. Math. 160(1) (1993), 43-51.
  • [10]  O. Kisi, F. Nuray, New convergence de nitions for sequences of sets, Abstr. Appl. Anal. 2013 (2013), Article ID 852796, 6 pages. doi:10.1155/2013/852796.
  • [11] P. Kostyrko, T. Salat, W. Wilczynski, I-Convergence, Real Anal. Exchange 26(2) (2000), 669-686.
  • [12] M. Mursaleen, O. H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288(1) (2003), 223-231.
  • [13] F. Nuray, B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math. 49 (2012), 8799.
  • [14] F. Nuray, W. H. Ruckle, Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245 (2000), 513-527.
  • [15] F. Nuray, E. Dundar, U. Ulusu, Wijsman I2-convergence of double sequences of closed sets, Pure and Applied Mathematics Letters, 2 (2014), 35-39.
  • [16] F. Nuray, E. Dundar, U. Ulusu, Wijsman statistical convergence of double sequences of sets, (under communication).
  • [17] F. Nuray, U. Ulusu, E. Dundar, Cesaro summability of double sequences of sets, Gen. Math. Notes 25(1) (2014), 8-18.
  • [18] F. Nuray, U. Ulusu, E. Dundar, Lacunary statistical convergence of double sequences of sets, Soft Computing 20(7) (2016), 2883-2888. doi:10.1007/s00500-015-1691-8.
  • [19] E. Savas, P. Das, A generalized statistical convergence via ideals, Appl. Math. Lett. 24(6) (2011), 826-830.
  • [20] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66(5) (1959), 361-375.
  • 21] Y. Sever,  O. Talo, On Statistical Convergence of Double Sequences of Closed Sets, Filomat 30(3) (2016), 533-539. doi:10.2298/FIL1603533S.
  • [22] Y. Sever,  O. Talo, B. Altay, On convergence of double sequences of closed sets, Contemporary Analysis and Applied M athematics 3(1) (2015), 30-49.
  • [23]  O. Talo, Y. Sever, F. Basar, On statistically convergent sequences of closed set, Filomat, 30(6) (2016), 1497-1509. doi:10.2298/FIL1606497T.
  • [24] U. Ulusu, E. Dundar, I-Lacunary statistical convergence of sequences of sets, Filomat 28(8) (2014), 1567-1574.
  • [25] U. Ulusu, F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics 4(2) (2012), 99-109.
  • [26] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc. 70(1) (1964), 186-188.
  • [27] R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions II, Trans. Amer. Math. Soc. 123(1) (1966), 32-45.
There are 27 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

ERDİNÇ Dündar This is me

UĞUR Ulusu

BÜNYAMİN Aydın

Publication Date April 1, 2017
Submission Date February 14, 2016
Acceptance Date July 23, 2016
Published in Issue Year 2017 Volume: 5 Issue: 1

Cite

APA Dündar, E., Ulusu, U., & Aydın, B. (2017). $I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS. Konuralp Journal of Mathematics, 5(1), 1-10.
AMA Dündar E, Ulusu U, Aydın B. $I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS. Konuralp J. Math. April 2017;5(1):1-10.
Chicago Dündar, ERDİNÇ, UĞUR Ulusu, and BÜNYAMİN Aydın. “$I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS”. Konuralp Journal of Mathematics 5, no. 1 (April 2017): 1-10.
EndNote Dündar E, Ulusu U, Aydın B (April 1, 2017) $I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS. Konuralp Journal of Mathematics 5 1 1–10.
IEEE E. Dündar, U. Ulusu, and B. Aydın, “$I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS”, Konuralp J. Math., vol. 5, no. 1, pp. 1–10, 2017.
ISNAD Dündar, ERDİNÇ et al. “$I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS”. Konuralp Journal of Mathematics 5/1 (April 2017), 1-10.
JAMA Dündar E, Ulusu U, Aydın B. $I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS. Konuralp J. Math. 2017;5:1–10.
MLA Dündar, ERDİNÇ et al. “$I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS”. Konuralp Journal of Mathematics, vol. 5, no. 1, 2017, pp. 1-10.
Vancouver Dündar E, Ulusu U, Aydın B. $I_2$-LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES OF SETS. Konuralp J. Math. 2017;5(1):1-10.
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