Year 2021,
Issue: 34, 20 - 27, 30.03.2021
Suma Pachilangode
,
Sunil Jacob John
References
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- 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.
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- 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.
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- 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.
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Convergence of Multiset Sequences
Year 2021,
Issue: 34, 20 - 27, 30.03.2021
Suma Pachilangode
,
Sunil Jacob John
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.