Asymptotically I-Cesaro equivalence of sequences of sets

Erdinç Dundar; Uğur Ulusu

doi:10.32323/ujma.409463

Research Article

Asymptotically I-Cesaro equivalence of sequences of sets

Year 2018, Volume: 1 Issue: 2, 101 - 105, 26.06.2018

Erdinç Dundar Uğur Ulusu

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

Cited By: 5

Abstract

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.

Keywords

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

References

[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.

Year 2018, Volume: 1 Issue: 2, 101 - 105, 26.06.2018

Erdinç Dundar Uğur Ulusu

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

Cited By: 5

Abstract

References

[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.

There are 22 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Articles
Authors	Erdinç Dundar Uğur Ulusu
Publication Date	June 26, 2018
Submission Date	March 26, 2018
Acceptance Date	April 2, 2018
Published in Issue	Year 2018 Volume: 1 Issue: 2

Cite

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. June 2018;1(2):101-105. doi:10.32323/ujma.409463
Chicago	Dundar, Erdinç, and Uğur Ulusu. “Asymptotically I-Cesaro Equivalence of Sequences of Sets”. Universal Journal of Mathematics and Applications 1, no. 2 (June 2018): 101-5. https://doi.org/10.32323/ujma.409463.
EndNote	Dundar E, Ulusu U (June 1, 2018) Asymptotically I-Cesaro equivalence of sequences of sets. Universal Journal of Mathematics and Applications 1 2 101–105.
IEEE	E. Dundar and U. Ulusu, “Asymptotically I-Cesaro equivalence of sequences of sets”, Univ. J. Math. Appl., vol. 1, no. 2, pp. 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 (June 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 and Uğur Ulusu. “Asymptotically I-Cesaro Equivalence of Sequences of Sets”. Universal Journal of Mathematics and Applications, vol. 1, no. 2, 2018, pp. 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.