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$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups

Year 2021, Volume: 4 Issue: 1, 45 - 48, 01.03.2021

Uğur Ulusu Fatih Nuray Erdinç Dündar

https://doi.org/10.33401/fujma.842104
Cited By: 4

Abstract

In this paper firstly, for functions defined on discrete countable amenable semigroups (DCASG), notions of $\mathfrak{I}$-limit and $\mathfrak{I}$-cluster points are introduced. Then, for the functions, notions of $\mathfrak{I}$-limit superior and inferior are examined.

Keywords

Amenable semigroups Folner sequence I-Convergence I-Cluster points I-Limit points

Supporting Institution

TÜBİTAK

Project Number

120F082

Thanks

This study is supported by TÜBİTAK (Scientific and Technological Research Council of Turkey) with the project number 120F082.

References

  • [1] P. Kostyrko, T. Salat, W. Wilczy´nski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [2] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443–464.
  • [3] K. Demirci, I-limit superior and limit inferior, Math. Commun., 6 (2001), 165–172.
  • [4] M. Day, Amenable semigroups, Illinois J. Math., 1 (1957), 509–544.
  • [5] S. A. Douglass, On a concept of summability in amenable semigroups, Math. Scand., 28 (1968), 96–102.
  • [6] P. F. Mah, Summability in amenable semigroups, Trans. Amer. Math. Soc., 156 (1971), 391–403.
  • [7] F. Nuray, B. E. Rhoades, Some kinds of convergence defined by Folner sequences, Analysis, 31(4) (2011), 381–390.
  • [8] E. Dündar, F. Nuray, U. Ulusu, I-convergent functions defined on amenable semigroups, (in review).
  • [9] I. Namioka, Følner’s conditions for amenable semigroups, Math. Scand., 15 (1964), 18–28.

Year 2021, Volume: 4 Issue: 1, 45 - 48, 01.03.2021

Uğur Ulusu Fatih Nuray Erdinç Dündar

https://doi.org/10.33401/fujma.842104
Cited By: 4

Abstract

Project Number

120F082

References

  • [1] P. Kostyrko, T. Salat, W. Wilczy´nski, I-convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [2] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak, I-convergence and extremal I-limit points, Math. Slovaca, 55 (2005), 443–464.
  • [3] K. Demirci, I-limit superior and limit inferior, Math. Commun., 6 (2001), 165–172.
  • [4] M. Day, Amenable semigroups, Illinois J. Math., 1 (1957), 509–544.
  • [5] S. A. Douglass, On a concept of summability in amenable semigroups, Math. Scand., 28 (1968), 96–102.
  • [6] P. F. Mah, Summability in amenable semigroups, Trans. Amer. Math. Soc., 156 (1971), 391–403.
  • [7] F. Nuray, B. E. Rhoades, Some kinds of convergence defined by Folner sequences, Analysis, 31(4) (2011), 381–390.
  • [8] E. Dündar, F. Nuray, U. Ulusu, I-convergent functions defined on amenable semigroups, (in review).
  • [9] I. Namioka, Følner’s conditions for amenable semigroups, Math. Scand., 15 (1964), 18–28.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Uğur Ulusu 0000-0001-7658-6114

Fatih Nuray 0000-0003-0160-4001

Erdinç Dündar 0000-0002-0545-7486

Project Number 120F082
Publication Date March 1, 2021
Submission Date December 16, 2020
Acceptance Date February 25, 2021
Published in Issue Year 2021 Volume: 4 Issue: 1

Cite

APA Ulusu, U., Nuray, F., & Dündar, E. (2021). $\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups. Fundamental Journal of Mathematics and Applications, 4(1), 45-48. https://doi.org/10.33401/fujma.842104
AMA Ulusu U, Nuray F, Dündar E. $\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups. FUJMA. March 2021;4(1):45-48. doi:10.33401/fujma.842104
Chicago Ulusu, Uğur, Fatih Nuray, and Erdinç Dündar. “$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups”. Fundamental Journal of Mathematics and Applications 4, no. 1 (March 2021): 45-48. https://doi.org/10.33401/fujma.842104.
EndNote Ulusu U, Nuray F, Dündar E (March 1, 2021) $\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups. Fundamental Journal of Mathematics and Applications 4 1 45–48.
IEEE U. Ulusu, F. Nuray, and E. Dündar, “$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups”, FUJMA, vol. 4, no. 1, pp. 45–48, 2021, doi: 10.33401/fujma.842104.
ISNAD Ulusu, Uğur et al. “$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups”. Fundamental Journal of Mathematics and Applications 4/1 (March 2021), 45-48. https://doi.org/10.33401/fujma.842104.
JAMA Ulusu U, Nuray F, Dündar E. $\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups. FUJMA. 2021;4:45–48.
MLA Ulusu, Uğur et al. “$\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups”. Fundamental Journal of Mathematics and Applications, vol. 4, no. 1, 2021, pp. 45-48, doi:10.33401/fujma.842104.
Vancouver Ulusu U, Nuray F, Dündar E. $\mathfrak{I}$-Limit and $\mathfrak{I}$-Cluster Points for Functions Defined on Amenable Semigroups. FUJMA. 2021;4(1):45-8.

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