Research Article
BibTex RIS Cite

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

Year 2023, Volume: 6 Issue: 2, 86 - 90, 01.07.2023

Erdinç Dündar Uğur Ulusu

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

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.

Year 2023, Volume: 6 Issue: 2, 86 - 90, 01.07.2023

Erdinç Dündar Uğur Ulusu

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

Abstract

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.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Erdinç Dündar 0000-0002-0545-7486

Uğur Ulusu 0000-0001-7658-6114

Publication Date July 1, 2023
Submission Date May 23, 2023
Acceptance Date June 30, 2023
Published in Issue Year 2023 Volume: 6 Issue: 2

Cite

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. July 2023;6(2):86-90. doi:10.32323/ujma.1301259
Chicago 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 6, no. 2 (July 2023): 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 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, 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 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 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, 2023, pp. 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.

Cited By

Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi
Afyon Kocatepe University Journal of Sciences and Engineering
https://doi.org/10.35414/akufemubid.1332740
On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence
Universal Journal of Mathematics and Applications
https://doi.org/10.32323/ujma.1376849
Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence
Mathematical Sciences and Applications E-Notes
https://doi.org/10.36753/mathenot.1330281
On rough continuity and rough $\mathcal{I}$-continuity of real functions
Novi Sad Journal of Mathematics
https://doi.org/10.30755/NSJOM.15197
 Download Cover Image

 23181

Universal Journal of Mathematics and Applications 

29207              

Creative Commons License  The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.