Asymptotically I-Cesaro equivalence of sequences of sets

Erdinç Dundar; Uğur Ulusu

doi:10.32323/ujma.409463

EN

Asymptotically I-Cesaro equivalence of sequences of sets

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Erdinç Dundar
Türkiye

Uğur Ulusu ^*
Türkiye

Publication Date

June 26, 2018

Submission Date

March 26, 2018

Acceptance Date

April 2, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

DOI

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

IZ

https://izlik.org/JA84RN36RU

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

1.Dundar E, Ulusu U. Asymptotically I-Cesaro equivalence of sequences of sets. Univ. J. Math. Appl. 2018;1(2):101-105. doi:10.32323/ujma.409463

Chicago

Dundar, Erdinç, and Uğur Ulusu. 2018. “Asymptotically I-Cesaro Equivalence of Sequences of Sets”. Universal Journal of Mathematics and Applications 1 (2): 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

[1]E. Dundar and U. Ulusu, “Asymptotically I-Cesaro equivalence of sequences of sets”, Univ. J. Math. Appl., vol. 1, no. 2, pp. 101–105, June 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 1, 2018): 101-105. https://doi.org/10.32323/ujma.409463.

JAMA

1.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, June 2018, pp. 101-5, doi:10.32323/ujma.409463.

Vancouver

1.Erdinç Dundar, Uğur Ulusu. Asymptotically I-Cesaro equivalence of sequences of sets. Univ. J. Math. Appl. 2018 Jun. 1;1(2):101-5. doi:10.32323/ujma.409463