Year 2017,
Volume: 5 Issue: 1, 1 - 10, 01.04.2017
ERDİNÇ Dündar
UĞUR Ulusu
,
BÜNYAMİN Aydın
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, Pacic J. Math. 160(1) (1993), 43-51.
- [10] O. Kisi, F. Nuray, New convergence denitions 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.
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, Pacic J. Math. 160(1) (1993), 43-51.
- [10] O. Kisi, F. Nuray, New convergence denitions 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.