$\mathfrak{I}$-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: 6

https://izlik.org/JA72PH33LE

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.