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

Yıl 2023, Cilt: 6 Sayı: 2, 86 - 90, 01.07.2023

Erdinç Dündar Uğur Ulusu

https://doi.org/10.32323/ujma.1301259
Cited By: 4

Öz

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.

Anahtar Kelimeler

Amenable semigroups Folner sequence Ideal Cauchy sequence Ideal convergence Rough convergence

Kaynakça

  • [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.

Yıl 2023, Cilt: 6 Sayı: 2, 86 - 90, 01.07.2023

Erdinç Dündar Uğur Ulusu

https://doi.org/10.32323/ujma.1301259
Cited By: 4

Öz

Kaynakça

  • [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.
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Erdinç Dündar 0000-0002-0545-7486

Uğur Ulusu 0000-0001-7658-6114

Yayımlanma Tarihi 1 Temmuz 2023
Gönderilme Tarihi 23 Mayıs 2023
Kabul Tarihi 30 Haziran 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 2

Kaynak Göster

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 Dündar E, Ulusu U. On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups. Univ. J. Math. Appl. Temmuz 2023;6(2):86-90. doi:10.32323/ujma.1301259
Chicago Dündar, Erdinç, ve Uğur Ulusu. “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”. Universal Journal of Mathematics and Applications 6, sy. 2 (Temmuz 2023): 86-90. https://doi.org/10.32323/ujma.1301259.
EndNote Dündar E, Ulusu U (01 Temmuz 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 E. Dündar ve U. Ulusu, “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”, Univ. J. Math. Appl., c. 6, sy. 2, ss. 86–90, 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 (Temmuz 2023), 86-90. https://doi.org/10.32323/ujma.1301259.
JAMA 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 ve Uğur Ulusu. “On Rough $\mathcal{I}$-Convergence and $\mathcal{I}$-Cauchy Sequence for Functions Defined on Amenable Semigroups”. Universal Journal of Mathematics and Applications, c. 6, sy. 2, 2023, ss. 86-90, doi:10.32323/ujma.1301259.
Vancouver 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.

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