Research Article
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Year 2024, Volume: 42 Issue: 5, 1575 - 1580, 04.10.2024

Abstract

References

  • REFERENCES
  • [1] Bender EA. Partitions of multisets. Discrete Math. 1974;9:301311. [CrossRef]
  • [2] Hickman JL. A note on the concept of multiset. Bull Aust Math Soc 1980;22:211217. [CrossRef]
  • [3] Lake J. Sets, fuzzy sets, multisets and functions. J Lond Math Soc 1976;2:323326. [CrossRef]
  • [4] Meyer RK, McRobbie MA. Multisets and relevant implication I and II. Australas J Philos 1982;60:107139. [CrossRef]
  • [5] Monro GP. The concept of multiset. Z Math Logik Grundlag Math 1987;33:171178. [CrossRef]
  • [6] Knuth D. The Art of Computer Programming: Seminumerical Algorithms. 2nd ed. Reading (MA): Addison-Wesley; 1981.
  • [7] Blizard WD. The development of multiset theory. Mod Log. 1991;1:319352.
  • [8] Blizard WD. Real-valued multisets and fuzzy sets. Fuzzy Sets Syst. 1989;33:7797. [CrossRef]
  • [9] Blizard WD. Multiset theory. Notre Dame J Form Log 1989;30:3666. [CrossRef]
  • [10] Syropoulos A. Mathematics of Multisets. Lect Notes Comput Sci 2001;2235:347358. [CrossRef]
  • [11] Ibrahim AM, Ejegwa PA. Multigroup actions on multisets. Ann Fuzzy Math Inform 2017;14:515526. [CrossRef]
  • [12] Majumdar P. Soft multisets. J Math Comput Sci 2012;2:17001711.
  • [13] Nazmul SK, Majumdar P, Samanta SK. On multisets and multigroups. Ann Fuzzy Math Inform 2013;6:643656.
  • [14] Singh D, Ibrahim AM, Yohanna T, Singh JN. An overview of the application of multiset. Novi Sad J Math 2007;37:7392.
  • [15] Pachilangode S, John SC. Convergence of multiset sequences. J New Theory 2021;34:2027.
  • [16] Zygmund A. Trigonometric Series. Cambridge (UK): Cambridge University Press; 1979.
  • [17] Fast H. Sur la convergence statistique. Colloq Math 1951;2:241244. [CrossRef]
  • [18] Steinhaus H. Sur la convergence ordiniaire et la convergence asymptotique. Colloq Math 1951;2:7384.
  • [19] Schoenberg IJ. The integrability of certain functions and related summability methods. Am Math Mon 1959;66:361375. [CrossRef]
  • [20] Erdös P, Tenenbaum G. Sur les densités de certaines suites d'entiers. Proc Lond Math Soc 1989;59:417438. [CrossRef]
  • [21] Freedman AR, Sember JJ. Densities and summability. Pac J Math. 1981;95:293305. [CrossRef]
  • [22] Miller HI. A measure theoretical subsequence characterization of statistical convergence. Trans Am Math Soc 1995;347:18111819. [CrossRef]
  • [23] Fridy JA. On statistical convergence. Colloq Math 1951;2:241244. [CrossRef]
  • [24] Gümüş H. Lacunary weak statistical convergence. Gen Math Notes 2015;28:5058.
  • [25] Gümüş H. A new approach to the concept of statistical convergence with the number of alpha. Commun Fac Sci Univ Ank Ser A1 2018;67:3745. [CrossRef]
  • [26] Kişi Ö. On lacunary arithmetic statistical convergence. J Appl Math Inform 2022;40:327339.
  • [27] Savaş E, Gürdal M. Statistical convergence in probabilistic normed spaces. UPB Sci Bull Ser A 2015;77:195204.
  • [28] Fridy JA, Orhan C. Lacunary statistical convergence. Pac J Math. 1993;160:4351. [CrossRef]
  • [29] Debnath S, Debnath A. Statistical convergence of multisequences on R. Appl Sci 2021;23:1728.
  • [30] Kostyrko P, Šalát T, Wileynski W. Convergence. Real Anal Exch 2000;26:669680. [CrossRef]
  • [31] Savaş E, Das P. A generalized statistical convergence via ideals. Appl Math Lett 2011;24:826830. [CrossRef]
  • [32] Das P, Savaş E. On statistical and lacunary statistical convergence of order. Bull Irani Math Soc. 2014;40:459472. [CrossRef]
  • [33] Das P, Savaş E, Ghosal S. On generalized summability methods using ideals. Appl Math Lett 2011;36:15091513. [CrossRef]
  • [34] Demir N, Gümüş H. Ideal convergence of multiset sequences. Filomat 2023;37:1019910207. [CrossRef]

A study on I-lacunary statistical convergence of multiset sequences

Year 2024, Volume: 42 Issue: 5, 1575 - 1580, 04.10.2024

Abstract

In classical set theory, elements of the set are written once but the sets in which the same item is repeated several times in daily life are in all areas of our lives. These sets are called multi-sets and are studied in many fields such as Mathematics, Physics, Chemistry, and Computer Sciences. Sequences consisting of elements of these sets are called multiset sequences. In this paper, we study the concept of I-lacunary statistical convergence of multiset sequences and investigate some important results.

References

  • REFERENCES
  • [1] Bender EA. Partitions of multisets. Discrete Math. 1974;9:301311. [CrossRef]
  • [2] Hickman JL. A note on the concept of multiset. Bull Aust Math Soc 1980;22:211217. [CrossRef]
  • [3] Lake J. Sets, fuzzy sets, multisets and functions. J Lond Math Soc 1976;2:323326. [CrossRef]
  • [4] Meyer RK, McRobbie MA. Multisets and relevant implication I and II. Australas J Philos 1982;60:107139. [CrossRef]
  • [5] Monro GP. The concept of multiset. Z Math Logik Grundlag Math 1987;33:171178. [CrossRef]
  • [6] Knuth D. The Art of Computer Programming: Seminumerical Algorithms. 2nd ed. Reading (MA): Addison-Wesley; 1981.
  • [7] Blizard WD. The development of multiset theory. Mod Log. 1991;1:319352.
  • [8] Blizard WD. Real-valued multisets and fuzzy sets. Fuzzy Sets Syst. 1989;33:7797. [CrossRef]
  • [9] Blizard WD. Multiset theory. Notre Dame J Form Log 1989;30:3666. [CrossRef]
  • [10] Syropoulos A. Mathematics of Multisets. Lect Notes Comput Sci 2001;2235:347358. [CrossRef]
  • [11] Ibrahim AM, Ejegwa PA. Multigroup actions on multisets. Ann Fuzzy Math Inform 2017;14:515526. [CrossRef]
  • [12] Majumdar P. Soft multisets. J Math Comput Sci 2012;2:17001711.
  • [13] Nazmul SK, Majumdar P, Samanta SK. On multisets and multigroups. Ann Fuzzy Math Inform 2013;6:643656.
  • [14] Singh D, Ibrahim AM, Yohanna T, Singh JN. An overview of the application of multiset. Novi Sad J Math 2007;37:7392.
  • [15] Pachilangode S, John SC. Convergence of multiset sequences. J New Theory 2021;34:2027.
  • [16] Zygmund A. Trigonometric Series. Cambridge (UK): Cambridge University Press; 1979.
  • [17] Fast H. Sur la convergence statistique. Colloq Math 1951;2:241244. [CrossRef]
  • [18] Steinhaus H. Sur la convergence ordiniaire et la convergence asymptotique. Colloq Math 1951;2:7384.
  • [19] Schoenberg IJ. The integrability of certain functions and related summability methods. Am Math Mon 1959;66:361375. [CrossRef]
  • [20] Erdös P, Tenenbaum G. Sur les densités de certaines suites d'entiers. Proc Lond Math Soc 1989;59:417438. [CrossRef]
  • [21] Freedman AR, Sember JJ. Densities and summability. Pac J Math. 1981;95:293305. [CrossRef]
  • [22] Miller HI. A measure theoretical subsequence characterization of statistical convergence. Trans Am Math Soc 1995;347:18111819. [CrossRef]
  • [23] Fridy JA. On statistical convergence. Colloq Math 1951;2:241244. [CrossRef]
  • [24] Gümüş H. Lacunary weak statistical convergence. Gen Math Notes 2015;28:5058.
  • [25] Gümüş H. A new approach to the concept of statistical convergence with the number of alpha. Commun Fac Sci Univ Ank Ser A1 2018;67:3745. [CrossRef]
  • [26] Kişi Ö. On lacunary arithmetic statistical convergence. J Appl Math Inform 2022;40:327339.
  • [27] Savaş E, Gürdal M. Statistical convergence in probabilistic normed spaces. UPB Sci Bull Ser A 2015;77:195204.
  • [28] Fridy JA, Orhan C. Lacunary statistical convergence. Pac J Math. 1993;160:4351. [CrossRef]
  • [29] Debnath S, Debnath A. Statistical convergence of multisequences on R. Appl Sci 2021;23:1728.
  • [30] Kostyrko P, Šalát T, Wileynski W. Convergence. Real Anal Exch 2000;26:669680. [CrossRef]
  • [31] Savaş E, Das P. A generalized statistical convergence via ideals. Appl Math Lett 2011;24:826830. [CrossRef]
  • [32] Das P, Savaş E. On statistical and lacunary statistical convergence of order. Bull Irani Math Soc. 2014;40:459472. [CrossRef]
  • [33] Das P, Savaş E, Ghosal S. On generalized summability methods using ideals. Appl Math Lett 2011;36:15091513. [CrossRef]
  • [34] Demir N, Gümüş H. Ideal convergence of multiset sequences. Filomat 2023;37:1019910207. [CrossRef]
There are 35 citations in total.

Details

Primary Language English
Subjects Clinical Chemistry
Journal Section Research Articles
Authors

Nihal Demir 0000-0002-2415-0674

Hafize Gumus 0000-0001-8972-5961

Publication Date October 4, 2024
Submission Date February 5, 2023
Published in Issue Year 2024 Volume: 42 Issue: 5

Cite

Vancouver Demir N, Gumus H. A study on I-lacunary statistical convergence of multiset sequences. SIGMA. 2024;42(5):1575-80.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/