Asymptotically I-Cesaro equivalence of sequences of sets

Erdinç Dundar; Uğur Ulusu

doi:10.32323/ujma.409463

Araştırma Makalesi

Asymptotically I-Cesaro equivalence of sequences of sets

Yıl 2018, Cilt: 1 Sayı: 2, 101 - 105, 26.06.2018

Erdinç Dundar Uğur Ulusu

https://doi.org/10.32323/ujma.409463

Cited By: 5

Öz

In this paper, we defined concepts of asymptotically $\mathcal{I}$-Cesaro equivalence and investigate the relationships between the concepts of asymptotically strongly $\mathcal{I}$-Cesaro equivalence, asymptotically strongly $\mathcal{I}$-lacunary equivalence, asymptotically $p$-strongly $ \mathcal{I}$-Cesaro equivalence and asymptotically $\mathcal{I}$-statistical equivalence of sequences of sets.

Anahtar Kelimeler

Asymptotically equivalence, Ces\`{a}ro summability, statistical convergence, lacunary sequence, ideal convergence, sequences of sets, Wijsman convergence.

Kaynakça

[1] M. Baronti and P. Papini, Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133-155), ISNM 76, Birkhauser, Basel (1986).
[2] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc., 31 (1985), 421–432.
[3] G. Beer, Wijsman convergence: A survey, Set-Valued Anal., 2 (1994), 77–94.
[4] P. Das, E. Savas¸ and S. Kr. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters, 24(9) (2011), 1509–1514.
[5] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
[6] J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math., 160(1) (1993), 43–51.
[7] Ö . Kişi and F. Nuray, New convergence definitions for sequences of sets, Abstr. Appl. Anal., 2013 (2013), Article ID 852796, 6 pages. http://dx.doi.org/10.1155/2013/852796.
[8] Ö . Kişi, E. Savas¸ and F. Nuray, On asymptotically I-lacunary statistical equivalence of sequences of sets, (submitted for publication).
[9] P. Kostyrko, T. ˇSalat and W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
[10] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Sci., 16(4) (1993), 755-762.
[11] F. Nuray and B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49 (2012), 87–99.
[12] R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Mathematica 36(1) (2003), 149-153.
[13] R. F. Patterson and E. Savas¸, On asymptotically lacunary statistically equivalent sequences, Thai J. Math., 4(2) (2006), 267–272.
[14] E. Savas¸, On I-asymptotically lacunary statistical equivalent sequences, Adv. Differ. Equ., 111 (2013), 7 pages. doi:10.1186/1687-1847-2013-111.
[15] E. Savas¸ and P. Das, A generalized statistical convergence via ideals, Appl. Math. Letters, 24(6) (2011), 826–830.
[16] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
[17] U. Ulusu and E. Dündar, I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567–1574. DOI 10.2298/FIL1408567U.
[18] U. Ulusu and F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics, 4(2) (2012), 99–109.
[19] U. Ulusu and F. Nuray, On asymptotically lacunary statistical equivalent set sequences, Journal of Mathematics, 2013 (2013), Article ID 310438, 5 pages. http://dx.doi.org/10.1155/2013/310438.
[20] U. Ulusu and Ö . Kişi, I-Cesa`ro summability of sequences of sets, Electronic Journal of Mathematical Analysis and Applications, 5(1) 2017, 278–286.
[21] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1) (1964), 186–188.
[22] R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions II, Trans. Amer. Math. Soc., 123(1) (1966), 32–45.

Yıl 2018, Cilt: 1 Sayı: 2, 101 - 105, 26.06.2018

Erdinç Dundar Uğur Ulusu

https://doi.org/10.32323/ujma.409463

Cited By: 5

Öz

Kaynakça

[1] M. Baronti and P. Papini, Convergence of sequences of sets, In: Methods of Functional Analysis in Approximation Theory (pp. 133-155), ISNM 76, Birkhauser, Basel (1986).
[2] G. Beer, On convergence of closed sets in a metric space and distance functions, Bull. Aust. Math. Soc., 31 (1985), 421–432.
[3] G. Beer, Wijsman convergence: A survey, Set-Valued Anal., 2 (1994), 77–94.
[4] P. Das, E. Savas¸ and S. Kr. Ghosal, On generalizations of certain summability methods using ideals, Appl. Math. Letters, 24(9) (2011), 1509–1514.
[5] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
[6] J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific J. Math., 160(1) (1993), 43–51.
[7] Ö . Kişi and F. Nuray, New convergence definitions for sequences of sets, Abstr. Appl. Anal., 2013 (2013), Article ID 852796, 6 pages. http://dx.doi.org/10.1155/2013/852796.
[8] Ö . Kişi, E. Savas¸ and F. Nuray, On asymptotically I-lacunary statistical equivalence of sequences of sets, (submitted for publication).
[9] P. Kostyrko, T. ˇSalat and W. Wilczy´nski, I-Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
[10] M. Marouf, Asymptotic equivalence and summability, Int. J. Math. Sci., 16(4) (1993), 755-762.
[11] F. Nuray and B. E. Rhoades, Statistical convergence of sequences of sets, Fasc. Math., 49 (2012), 87–99.
[12] R. F. Patterson, On asymptotically statistically equivalent sequences, Demostratio Mathematica 36(1) (2003), 149-153.
[13] R. F. Patterson and E. Savas¸, On asymptotically lacunary statistically equivalent sequences, Thai J. Math., 4(2) (2006), 267–272.
[14] E. Savas¸, On I-asymptotically lacunary statistical equivalent sequences, Adv. Differ. Equ., 111 (2013), 7 pages. doi:10.1186/1687-1847-2013-111.
[15] E. Savas¸ and P. Das, A generalized statistical convergence via ideals, Appl. Math. Letters, 24(6) (2011), 826–830.
[16] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
[17] U. Ulusu and E. Dündar, I-lacunary statistical convergence of sequences of sets, Filomat, 28(8) (2014), 1567–1574. DOI 10.2298/FIL1408567U.
[18] U. Ulusu and F. Nuray, Lacunary statistical convergence of sequence of sets, Progress in Applied Mathematics, 4(2) (2012), 99–109.
[19] U. Ulusu and F. Nuray, On asymptotically lacunary statistical equivalent set sequences, Journal of Mathematics, 2013 (2013), Article ID 310438, 5 pages. http://dx.doi.org/10.1155/2013/310438.
[20] U. Ulusu and Ö . Kişi, I-Cesa`ro summability of sequences of sets, Electronic Journal of Mathematical Analysis and Applications, 5(1) 2017, 278–286.
[21] R. A. Wijsman, Convergence of sequences of convex sets, cones and functions, Bull. Amer. Math. Soc., 70(1) (1964), 186–188.
[22] R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions II, Trans. Amer. Math. Soc., 123(1) (1966), 32–45.

Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil	İngilizce
Konular	Matematik
Bölüm	Makaleler
Yazarlar	Erdinç Dundar Uğur Ulusu
Yayımlanma Tarihi	26 Haziran 2018
Gönderilme Tarihi	26 Mart 2018
Kabul Tarihi	2 Nisan 2018
Yayımlandığı Sayı	Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA	Dundar, E., & Ulusu, U. (2018). Asymptotically I-Cesaro equivalence of sequences of sets. Universal Journal of Mathematics and Applications, 1(2), 101-105. https://doi.org/10.32323/ujma.409463
AMA	Dundar E, Ulusu U. Asymptotically I-Cesaro equivalence of sequences of sets. Univ. J. Math. Appl. Haziran 2018;1(2):101-105. doi:10.32323/ujma.409463
Chicago	Dundar, Erdinç, ve Uğur Ulusu. “Asymptotically I-Cesaro Equivalence of Sequences of Sets”. Universal Journal of Mathematics and Applications 1, sy. 2 (Haziran 2018): 101-5. https://doi.org/10.32323/ujma.409463.
EndNote	Dundar E, Ulusu U (01 Haziran 2018) Asymptotically I-Cesaro equivalence of sequences of sets. Universal Journal of Mathematics and Applications 1 2 101–105.
IEEE	E. Dundar ve U. Ulusu, “Asymptotically I-Cesaro equivalence of sequences of sets”, Univ. J. Math. Appl., c. 1, sy. 2, ss. 101–105, 2018, doi: 10.32323/ujma.409463.
ISNAD	Dundar, Erdinç - Ulusu, Uğur. “Asymptotically I-Cesaro Equivalence of Sequences of Sets”. Universal Journal of Mathematics and Applications 1/2 (Haziran 2018), 101-105. https://doi.org/10.32323/ujma.409463.
JAMA	Dundar E, Ulusu U. Asymptotically I-Cesaro equivalence of sequences of sets. Univ. J. Math. Appl. 2018;1:101–105.
MLA	Dundar, Erdinç ve Uğur Ulusu. “Asymptotically I-Cesaro Equivalence of Sequences of Sets”. Universal Journal of Mathematics and Applications, c. 1, sy. 2, 2018, ss. 101-5, doi:10.32323/ujma.409463.
Vancouver	Dundar E, Ulusu U. Asymptotically I-Cesaro equivalence of sequences of sets. Univ. J. Math. Appl. 2018;1(2):101-5.