On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups

Erdinç Dündar; Uğur Ulusu

doi:10.32323/ujma.1301259

EN

On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups

Abstract

In this paper, firstly we introduced the concepts of rough $\mathcal{I}$-convergence, rough $\mathcal{I}^*$-convergence, rough $\mathcal{I}$-Cauchy sequence, and rough $\mathcal{I}^*$-Cauchy sequence of a function defined on discrete countable amenable semigroups. Then, we investigated the relations between them.

Keywords

Amenable semigroups, Folner sequence, Ideal Cauchy sequence, Ideal convergence, Rough convergence

References

[1] P. Kostyrko, T. Salat, W. Wilczynski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
[2] H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Opt., 22 (2001), 199–222.
[3] H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numer. Funct. Anal. Opt., 24 (2003), 285–301.
[4] M. Arslan, E. Dündar, Rough convergence in 2-normed spaces, Bull. Math. Anal. Appl., 10(3) (2018), 1–9.
[5] M. Arslan, E. Dündar, On rough convergence in 2-normed spaces and some properties, Filomat, 33(16) (2019), 5077–5086.
[6] M. Arslan, E. Dündar, Rough statistical convergence in 2-normed spaces, Honam Mathematical J., 43(3) (2021), 417–431.
[7] S. Aytar, Rough statistical convergence, Numer. Funct. Anal. and Optimiz., 29(3-4) (2008), 291–303.
[8] E. Dündar, C. C， akan, Rough I-convergence, Gulf J. Math., 2(1) (2014), 45–51.
[9] M. Day, Amenable semigroups, Illinois J. Math., 1 (1957), 509–544.
[10] S. A. Douglass, Summing sequences for amenable semigroups, Michigan Math. J., 20 (1973), 169–179.

[11] P. F. Mah, Summability in amenable semigroups, Trans. Amer. Math. Soc., 156 (1971), 391–403.
[12] P. F. Mah, Matrix summability in amenable semigroups, Proc. Amer. Math. Soc., 36 (1972), 414–420.
[13] S. A. Douglass, On a concept of summability in amenable semigroups, Math. Scand., 28 (1968), 96–102.
[14] F. Nuray, B. E. Rhoades, Some kinds of convergence defined by Folner sequences, Analysis, 31(4) (2011), 381–390.
[15] E. Dündar, U. Ulusu, F. Nuray, Rough convergent functions defined on amenable semigroups, Sigma J. Eng. Nat. Sci. (accepted - in press).
[16] E. Dündar, U. Ulusu, On rough convergence in amenable semigroups and some properties, J. Intell. Fuzzy Syst., 41 (2021), 2319–2324.
[17] E. Dündar, U. Ulusu, Rough statistical convergent functions defined on amenable semigroups, (under review).
[18] E. Dündar, U. Ulusu, S， . Yalvac，, N. Akın, Rough ideal convergent functions defined on amenable semigroups, (under review).
[19] E. Dündar, F. Nuray, U. Ulusu, I-convergent functions defined on amenable semigroups, TWMS J. Pure Appl. Math. (accepted - in press).
[20] U. Ulusu, F. Nuray, E. Dündar, I-limit and I-cluster points for functions defined on amenable semigroups, Fundam. J. Math. Appl., 4(1) (2021), 45–48.
[21] U. Ulusu, E. Dündar, F. Nuray, Some generalized convergence types using ideals in amenable semigroups, Bull. Math. Anal. Appl., 11(1) (2019), 28–35.
[22] U. Ulusu, E. Dündar, B. Aydın, Asymptotically I-statistical equivalent functions defined on amenable semigroups, Sigma J. Eng. Nat. Sci., 37(4) (2019), 1367–1373.
[23] E. Dündar, C. Çakan, Rough convergence of double sequences, Demonstr. Math., 47(3) (2014), 638–651.
[24] E. Dündar, On Rough I2-convergence, Numer. Funct. Anal. Optim., 37(4) (2016), 480–491.
[25] A. Nabiev, S. Pehlivan, M. Gürdal, On I-Cauchy Sequences, Taiwanese J. Math., 11(2) (2007), 569–576.
[26] I. Namioka, Folner’s conditions for amenable semigroups, Math. Scand., 15 (1964), 18–28.
[27] H. X. Phu, Rough continuity of linear operators, Numer. Funct. Anal. Optim., 23 (2002), 139–146.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Erdinç Dündar ^*
0000-0002-0545-7486
Türkiye

Uğur Ulusu
0000-0001-7658-6114
Türkiye

Publication Date

July 1, 2023

Submission Date

May 23, 2023

Acceptance Date

June 30, 2023

Published in Issue

Year 2023 Volume: 6 Number: 2

DOI

https://doi.org/10.32323/ujma.1301259

IZ

https://izlik.org/JA28JB64JA

APA

Dündar, E., & Ulusu, U. (2023). On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups. Universal Journal of Mathematics and Applications, 6(2), 86-90. https://doi.org/10.32323/ujma.1301259

AMA

1.Dündar E, Ulusu U. On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups. Univ. J. Math. Appl. 2023;6(2):86-90. doi:10.32323/ujma.1301259

Chicago

Dündar, Erdinç, and Uğur Ulusu. 2023. “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”. Universal Journal of Mathematics and Applications 6 (2): 86-90. https://doi.org/10.32323/ujma.1301259.

EndNote

Dündar E, Ulusu U (July 1, 2023) On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups. Universal Journal of Mathematics and Applications 6 2 86–90.

IEEE

[1]E. Dündar and U. Ulusu, “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”, Univ. J. Math. Appl., vol. 6, no. 2, pp. 86–90, July 2023, doi: 10.32323/ujma.1301259.

ISNAD

Dündar, Erdinç - Ulusu, Uğur. “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”. Universal Journal of Mathematics and Applications 6/2 (July 1, 2023): 86-90. https://doi.org/10.32323/ujma.1301259.

JAMA

1.Dündar E, Ulusu U. On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups. Univ. J. Math. Appl. 2023;6:86–90.

MLA

Dündar, Erdinç, and Uğur Ulusu. “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”. Universal Journal of Mathematics and Applications, vol. 6, no. 2, July 2023, pp. 86-90, doi:10.32323/ujma.1301259.

Vancouver

1.Erdinç Dündar, Uğur Ulusu. On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups. Univ. J. Math. Appl. 2023 Jul. 1;6(2):86-90. doi:10.32323/ujma.1301259