Research Article

Convergence of Multiset Sequences

Number: 34 March 30, 2021
EN

Convergence of Multiset Sequences

Abstract

In this paper, we introduce the concept of the multiset sequence and its convergence. A few special examples of multiset sequences, e.g. a prime identifier, are also given. A metric is defined in multisets for statistical convergences of multiset sequences. Wijsman and Hausdorff convergence of multiset sequences are discussed.

Keywords

Multiset, multiset sequence, prime identifier sequence, set theoretic limit, Wijsman convergence, Hausdorff convergence

References

  1. D. E. Knuth, The Art of Computer Programming, Seminumerical Algorithms, Addison-Wesley 2 (1981).
  2. E. A. Bender, Partitions of Multisets, Discrete Mathematics (1974) 301-311. C. S. Calude, G. Paun, G. Rozenberg, A. Salomaa, Multiset Processing LNCS 2235, Springer Verlag (2001) 347-358.
  3. A. Syropoulos, Mathematics of Multisets, In: Calude C.S., Paun G., Rozenberg G., Salomaa A. (eds) Multiset Processing. WMC 2000. Lecture Notes in Computer Science, Springer, Berlin, Heidelberg 2235 (2001).
  4. N. J. Wildberger, A New Look at Multisets, School of Mathematics, UNSW Sydney 2053 (2003).
  5. D. Singh, A. M. Ibrahim, T. Yohanna, J. N. Singh, An Overview of The Application of Multiset, Novi Sad Journal of Mathematics 37 (2007) 73-92.
  6. K. P. Girish, S. J. John, Rough Multisets and Information Multisystems, Advances in Decision Sciences Article ID 495392 2011 (2011) 17 pages.
  7. R. R. Yager, On the Theory of Bags, International Journal of General Systems 13 (1986) 23-37.
  8. S. P. Jena, S. K. Ghosh, B. K. Tripathy, On the Theory of Bags and Lists, Information Sciences 132 (2001) 241-254.
  9. C. Brink, Multisets and the Algebra of Relevance logic, Non-Classical Logic 5 (1988) 75-95. K. P. Girish, S. J. John, Relations and Functions in Multiset Context, Information Sciences 179 (2009) 758-768.
  10. U. Ulusu, E. Dündar, I-Lacunary Statistical Convergence of Sequences of Sets, Filomat 28(8) (2014) 1567-1574.
APA
Pachilangode, S., & John, S. J. (2021). Convergence of Multiset Sequences. Journal of New Theory, 34, 20-27. https://izlik.org/JA77MH28FG
AMA
1.Pachilangode S, John SJ. Convergence of Multiset Sequences. JNT. 2021;(34):20-27. https://izlik.org/JA77MH28FG
Chicago
Pachilangode, Suma, and Sunil Jacob John. 2021. “Convergence of Multiset Sequences”. Journal of New Theory, nos. 34: 20-27. https://izlik.org/JA77MH28FG.
EndNote
Pachilangode S, John SJ (March 1, 2021) Convergence of Multiset Sequences. Journal of New Theory 34 20–27.
IEEE
[1]S. Pachilangode and S. J. John, “Convergence of Multiset Sequences”, JNT, no. 34, pp. 20–27, Mar. 2021, [Online]. Available: https://izlik.org/JA77MH28FG
ISNAD
Pachilangode, Suma - John, Sunil Jacob. “Convergence of Multiset Sequences”. Journal of New Theory. 34 (March 1, 2021): 20-27. https://izlik.org/JA77MH28FG.
JAMA
1.Pachilangode S, John SJ. Convergence of Multiset Sequences. JNT. 2021;:20–27.
MLA
Pachilangode, Suma, and Sunil Jacob John. “Convergence of Multiset Sequences”. Journal of New Theory, no. 34, Mar. 2021, pp. 20-27, https://izlik.org/JA77MH28FG.
Vancouver
1.Suma Pachilangode, Sunil Jacob John. Convergence of Multiset Sequences. JNT [Internet]. 2021 Mar. 1;(34):20-7. Available from: https://izlik.org/JA77MH28FG