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## Convergence of Multiset Sequences

#### Suma PACHİLANGODE [1] , Sunil Jacob JOHN [2]

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.
Multiset, multiset sequence, prime identifier sequence, set theoretic limit, Wijsman convergence, Hausdorff convergence
• 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.
Primary Language en Mathematics Research Article Orcid: 0000-0001-6764-6832Author: Suma PACHİLANGODE (Primary Author)Institution: National Institute of Technology, CalicutCountry: India Orcid: 0000-0002-6333-2884Author: Sunil Jacob JOHNInstitution: NATIONAL INSTITUTE OF TECHNOLOGY, CALICUT, KERLA.Country: India Publication Date : March 30, 2021
 Bibtex @research article { jnt689917, journal = {Journal of New Theory}, issn = {}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2021}, volume = {}, pages = {20 - 27}, doi = {}, title = {Convergence of Multiset Sequences}, key = {cite}, author = {Pachilangode, Suma and John, Sunil Jacob} } APA Pachilangode, S , John, S . (2021). Convergence of Multiset Sequences . Journal of New Theory , (34) , 20-27 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/61070/689917 MLA Pachilangode, S , John, S . "Convergence of Multiset Sequences" . Journal of New Theory (2021 ): 20-27 Chicago Pachilangode, S , John, S . "Convergence of Multiset Sequences". Journal of New Theory (2021 ): 20-27 RIS TY - JOUR T1 - Convergence of Multiset Sequences AU - Suma Pachilangode , Sunil Jacob John Y1 - 2021 PY - 2021 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 20 EP - 27 VL - IS - 34 SN - -2149-1402 M3 - UR - Y2 - 2021 ER - EndNote %0 Journal of New Theory Convergence of Multiset Sequences %A Suma Pachilangode , Sunil Jacob John %T Convergence of Multiset Sequences %D 2021 %J Journal of New Theory %P -2149-1402 %V %N 34 %R %U ISNAD Pachilangode, Suma , John, Sunil Jacob . "Convergence of Multiset Sequences". Journal of New Theory / 34 (March 2021): 20-27 . AMA Pachilangode S , John S . Convergence of Multiset Sequences. JNT. 2021; (34): 20-27. Vancouver Pachilangode S , John S . Convergence of Multiset Sequences. Journal of New Theory. 2021; (34): 20-27. IEEE S. Pachilangode and S. John , "Convergence of Multiset Sequences", Journal of New Theory, no. 34, pp. 20-27, Mar. 2021

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