Research Article
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Year 2021, Issue: 34, 20 - 27, 30.03.2021
https://izlik.org/JA77MH28FG

Abstract

References

  • D. E. Knuth, The Art of Computer Programming, Seminumerical Algorithms, Addison-Wesley 2 (1981).
  • 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.
  • 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).
  • N. J. Wildberger, A New Look at Multisets, School of Mathematics, UNSW Sydney 2053 (2003).
  • 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.
  • K. P. Girish, S. J. John, Rough Multisets and Information Multisystems, Advances in Decision Sciences Article ID 495392 2011 (2011) 17 pages.
  • R. R. Yager, On the Theory of Bags, International Journal of General Systems 13 (1986) 23-37.
  • S. P. Jena, S. K. Ghosh, B. K. Tripathy, On the Theory of Bags and Lists, Information Sciences 132 (2001) 241-254.
  • 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.
  • U. Ulusu, E. Dündar, I-Lacunary Statistical Convergence of Sequences of Sets, Filomat 28(8) (2014) 1567-1574.
  • A. R. Benson, R. Kumar, A. Tomkins, Sequences of Sets, International Conference on Knowledge Discovery and Data Mining (2018) 19-23 London, United Kingdom.
  • H. Gumus, On Wijsman Ideal Convergent Set of Sequences Defined by an Orlicz Function, Filomat 30(13) (2016) 3501-3509.
  • O. Talo, Y. Sever, On Kuratowski I-Convergence of Sequences of Closed Sets, Filomat 31(4) (2017) 899-912.
  • M. Baronti, P. Papini, Convergence of Sequences of Sets, Methods of Functional Analysis in Approximation Theory 76 (1986) 133-155.
  • R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions. II, Transactions of the American Mathematical Society 123(1) (1966) 32-45.
  • F. Nuray, B. E. Rhoades, Statistical Convergence of Sequences of Sets, Fasciculi Mathematici 49 (2012) 87-99.

Convergence of Multiset Sequences

Year 2021, Issue: 34, 20 - 27, 30.03.2021
https://izlik.org/JA77MH28FG

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.

References

  • D. E. Knuth, The Art of Computer Programming, Seminumerical Algorithms, Addison-Wesley 2 (1981).
  • 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.
  • 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).
  • N. J. Wildberger, A New Look at Multisets, School of Mathematics, UNSW Sydney 2053 (2003).
  • 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.
  • K. P. Girish, S. J. John, Rough Multisets and Information Multisystems, Advances in Decision Sciences Article ID 495392 2011 (2011) 17 pages.
  • R. R. Yager, On the Theory of Bags, International Journal of General Systems 13 (1986) 23-37.
  • S. P. Jena, S. K. Ghosh, B. K. Tripathy, On the Theory of Bags and Lists, Information Sciences 132 (2001) 241-254.
  • 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.
  • U. Ulusu, E. Dündar, I-Lacunary Statistical Convergence of Sequences of Sets, Filomat 28(8) (2014) 1567-1574.
  • A. R. Benson, R. Kumar, A. Tomkins, Sequences of Sets, International Conference on Knowledge Discovery and Data Mining (2018) 19-23 London, United Kingdom.
  • H. Gumus, On Wijsman Ideal Convergent Set of Sequences Defined by an Orlicz Function, Filomat 30(13) (2016) 3501-3509.
  • O. Talo, Y. Sever, On Kuratowski I-Convergence of Sequences of Closed Sets, Filomat 31(4) (2017) 899-912.
  • M. Baronti, P. Papini, Convergence of Sequences of Sets, Methods of Functional Analysis in Approximation Theory 76 (1986) 133-155.
  • R. A. Wijsman, Convergence of Sequences of Convex Sets, Cones and Functions. II, Transactions of the American Mathematical Society 123(1) (1966) 32-45.
  • F. Nuray, B. E. Rhoades, Statistical Convergence of Sequences of Sets, Fasciculi Mathematici 49 (2012) 87-99.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Suma Pachilangode 0000-0001-6764-6832

Sunil Jacob John 0000-0002-6333-2884

Submission Date February 17, 2020
Publication Date March 30, 2021
IZ https://izlik.org/JA77MH28FG
Published in Issue Year 2021 Issue: 34

Cite

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


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