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RESULTS ON SOFT HILBERT SPACES

Yıl 2019, Cilt: 9 Sayı: 1, 159 - 164, 01.03.2019

Öz

Molodtsov [6] introduced the notion of soft set which can be considered as a new mathematical approach for vagueness. Das and Samanta [8] rst de ned the soft vector space and soft norm. Yazar and et al. [9] de ned the soft vector space by using the concept of soft point given in [4, 5] and introduced the soft normed spaces in a new point of view. In the present paper, We give some properties of soft inner product spaces and present some examples for soft inner product spaces. Soft Hilbert space is introduced and some related properties are investigated. Finally, soft ~`2 space is given as an example for soft Hilbert spaces.

Kaynakça

  • [1] S. Das, P. Majumdar, S.K. Samanta, (2015), On soft lineer spaces and soft normed lineer spaces, Annals of Fuzzy. Math. and Inf., 9(1), pp. 91-109.
  • [2] S. Das and S. K. Samanta, (2013), Soft linear operators in soft normed linear spaces, Ann. Fuzzy Math. Inform., 6(2), pp. 295-314.
  • [3] S. Das and S. K. Samanta, (2012), Soft real sets, soft real numbers and their properties, J. Fuzzy Math., 20(3), pp. 551-576.
  • [4] S. Bayramov, C.Gunduz,(2013), Soft locally compact spaces and soft paracompact spaces, Journal of Math. and Sys. Sci., 3, pp. 122-130.
  • [5] S. Das, S.K.Samanta,(2013), Soft Metric, Annals of Fuzzy. Math. and Inf., 6(1), pp. 77-94.
  • [6] D. Molodtsov, (1999), Soft set theory- first results, Comput. Math. Appl., 37, pp. 19-31.
  • [7] S. Das, S. K. Samanta, (2013), On soft inner product spaces,Ann. Fuzzy Math. Inform., 6(1), pp. 151-170.
  • [8] S. Das and S. K. Samanta, (2013), On soft metric spaces, J. Fuzzy Math., 21, pp. 707-734.
  • [9] M. I. Yazar, T. Bilgin, S. Bayramov, C. Gunduz, (2014), A new view on soft normed spaces, International Mathematical Forum, 9(24), pp. 1149 1159.
  • [10] Y. B. Jun, C. H. Park, (2009), Application of soft sets in Hilbert Algebras, Iranian Journal of Fuzzy Systems, 6(2), pp. 75-86.
  • [11] s. Das,S. K. Samanta, (2014), Operators on soft inner product spaces, Fuzzy Inf. Eng., 6, pp. 435-450.
  • [12] s. Das,S. K. Samanta, (2014), Operators on soft inner product spaces II, Ann. Fuzzy Math. Inform., 13(3), pp. 297-315
  • [13] N. Xie, (2015), Soft points and the structure of soft topological spaces, Ann. Fuzzy Math. Inform., 10(2), pp. 309-322.
Yıl 2019, Cilt: 9 Sayı: 1, 159 - 164, 01.03.2019

Öz

Kaynakça

  • [1] S. Das, P. Majumdar, S.K. Samanta, (2015), On soft lineer spaces and soft normed lineer spaces, Annals of Fuzzy. Math. and Inf., 9(1), pp. 91-109.
  • [2] S. Das and S. K. Samanta, (2013), Soft linear operators in soft normed linear spaces, Ann. Fuzzy Math. Inform., 6(2), pp. 295-314.
  • [3] S. Das and S. K. Samanta, (2012), Soft real sets, soft real numbers and their properties, J. Fuzzy Math., 20(3), pp. 551-576.
  • [4] S. Bayramov, C.Gunduz,(2013), Soft locally compact spaces and soft paracompact spaces, Journal of Math. and Sys. Sci., 3, pp. 122-130.
  • [5] S. Das, S.K.Samanta,(2013), Soft Metric, Annals of Fuzzy. Math. and Inf., 6(1), pp. 77-94.
  • [6] D. Molodtsov, (1999), Soft set theory- first results, Comput. Math. Appl., 37, pp. 19-31.
  • [7] S. Das, S. K. Samanta, (2013), On soft inner product spaces,Ann. Fuzzy Math. Inform., 6(1), pp. 151-170.
  • [8] S. Das and S. K. Samanta, (2013), On soft metric spaces, J. Fuzzy Math., 21, pp. 707-734.
  • [9] M. I. Yazar, T. Bilgin, S. Bayramov, C. Gunduz, (2014), A new view on soft normed spaces, International Mathematical Forum, 9(24), pp. 1149 1159.
  • [10] Y. B. Jun, C. H. Park, (2009), Application of soft sets in Hilbert Algebras, Iranian Journal of Fuzzy Systems, 6(2), pp. 75-86.
  • [11] s. Das,S. K. Samanta, (2014), Operators on soft inner product spaces, Fuzzy Inf. Eng., 6, pp. 435-450.
  • [12] s. Das,S. K. Samanta, (2014), Operators on soft inner product spaces II, Ann. Fuzzy Math. Inform., 13(3), pp. 297-315
  • [13] N. Xie, (2015), Soft points and the structure of soft topological spaces, Ann. Fuzzy Math. Inform., 10(2), pp. 309-322.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

M. I. Yazar Bu kişi benim

C. G. Aras Bu kişi benim

S. Bayramov Bu kişi benim

Yayımlanma Tarihi 1 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 1

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