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Fixed Points Of Mappings On The Fuzzy Reflexive Spaces

Year 2015, Volume: 28 Issue: 4, 729 - 735, 16.12.2015

Abstract

In this paper we first define the new notion of fuzzy uniform normal structure. Moreover, it is proved that the spectrum of the category of fuzzy reexive spaces is broader than the category of the spaces has fuzzy normal structure. Also, we introduce the notions of FNST, FNSTN  and we prove the theorems of the fixed points of some classes of mappings on the sets from the fuzzy reflexive space, which have some of the properties FNST, FNSTN.

 

References

  • Bag, T., “Some fundamental theorems in Felbin’s type fuzzy normed linear spaces”, International Journal of Mathematics and Scientific Computing, 1 (2): 44-49, (2011).
  • Bag, T. and Samanta, S. K., “Fixed point theorems in Felbin’s type fuzzy normed linear spaces” , J. Fuzzy Math. , 16 (1): 243-260, (2008).
  • Bag, T. and Samanta, S. K., “Fixed point theorems in fuzzy normed linear spaces”, Information Sciences, 176: 2910-2931, (2006).
  • Bag, T. and Samanta, S. K., “fuzzy bounded linear operators in Felbin’s type fuzzy normed linear spaces”, Fuzzy Sets and Systems 159: 685-707, (2008).
  • Bag, T. and Samanta, S K., “Fuzzy reflexivity of Felbin’s type fuzzy normed linear spaces and fixed point theorems in such spaces” , Iranian Journal of Fuzzy Systems, 8 (5): 103-115, (2011).
  • Baillon, J. B. and Schoneberg, R.,“ Asymptotic normal structure and fixed points of nonexpansive mappings”, Proc. Am. Math. Soc., 81: 257-264, (1981).
  • Felbin, C.,“Finite dimensional fuzzy normed linear space”, Fuzzy Sets and Systems, 48: 239-248, (1992).
  • Hasankhani, A., Nazari, A. and Saheli, M.,“ Some properties of fuzzy Hilbert spaces and norm of operators”, Iranian Journal of Fuzzy Systems, 7 (3): 129-157, (2010).
  • Kaleva , O . and Seikkala , S ., “On fuzzy metric spaces”, Fuzzy Sets and Systems, 12 : 215-229, (1984) .
  • Kiany , F . and Amini-Harandi , A ., “ Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces”, Fixed Point Theory and Applications , 2011 ( 94 ): 1-10, (2011) .
  • Kirk, W. A ., “A fixed point theorem for mappings which Amer . Math . Monthly , 72 : 1004-1006, (1965). increase distance”,
  • Mijajlovic , B ., “Fixed points of mapping on the normed and reflexive spaces”, Kragujevac J . Math . ‎29 : 113-120 .) 2006( ,
  • Mizumoto , M . and Tanaka , J ., “Some properties of fuzzy numbers in : M . M . Gupta et al . Editors” , Advances Applications , North-Holland , New-York : 153- 164, (1979) . Set Theory and
  • Sadeqi , I . and Solaty kia , F ., “Some fixed point theorems in fuzzy reflexive Banach spaces” , Chaos , Solitons and Fractals , 41 : 2606-2612 (2009) .
  • Sadeqi , I ., Moradlou , F . and Salehi , M ., “On approximate cauchy equation in Felbin's type fuzzy normed linear spaces” , Iranian Journal of Fuzzy Systems , 10 (3) : 51-63, (2013).
  • Smulian , V .,“ On the principle of inclusion in the space of the type (B)”, Math . Sb . (N . S . ) , 5: 237-238 , (1939) .
  • Vajzovic , F . and Stefanovic , M ., “Two fixed point theorems”, Radovi Akad . Nauka Bosnei Herceg. , 24: 63-71, (1985) .
  • Xiao , J . and Zhu , X ., “On linearly topological structure and property of fuzzy normed linear space”, Fuzzy Sets and Systems, 125: 153-161, (2002).
Year 2015, Volume: 28 Issue: 4, 729 - 735, 16.12.2015

Abstract

References

  • Bag, T., “Some fundamental theorems in Felbin’s type fuzzy normed linear spaces”, International Journal of Mathematics and Scientific Computing, 1 (2): 44-49, (2011).
  • Bag, T. and Samanta, S. K., “Fixed point theorems in Felbin’s type fuzzy normed linear spaces” , J. Fuzzy Math. , 16 (1): 243-260, (2008).
  • Bag, T. and Samanta, S. K., “Fixed point theorems in fuzzy normed linear spaces”, Information Sciences, 176: 2910-2931, (2006).
  • Bag, T. and Samanta, S. K., “fuzzy bounded linear operators in Felbin’s type fuzzy normed linear spaces”, Fuzzy Sets and Systems 159: 685-707, (2008).
  • Bag, T. and Samanta, S K., “Fuzzy reflexivity of Felbin’s type fuzzy normed linear spaces and fixed point theorems in such spaces” , Iranian Journal of Fuzzy Systems, 8 (5): 103-115, (2011).
  • Baillon, J. B. and Schoneberg, R.,“ Asymptotic normal structure and fixed points of nonexpansive mappings”, Proc. Am. Math. Soc., 81: 257-264, (1981).
  • Felbin, C.,“Finite dimensional fuzzy normed linear space”, Fuzzy Sets and Systems, 48: 239-248, (1992).
  • Hasankhani, A., Nazari, A. and Saheli, M.,“ Some properties of fuzzy Hilbert spaces and norm of operators”, Iranian Journal of Fuzzy Systems, 7 (3): 129-157, (2010).
  • Kaleva , O . and Seikkala , S ., “On fuzzy metric spaces”, Fuzzy Sets and Systems, 12 : 215-229, (1984) .
  • Kiany , F . and Amini-Harandi , A ., “ Fixed point and endpoint theorems for set-valued fuzzy contraction maps in fuzzy metric spaces”, Fixed Point Theory and Applications , 2011 ( 94 ): 1-10, (2011) .
  • Kirk, W. A ., “A fixed point theorem for mappings which Amer . Math . Monthly , 72 : 1004-1006, (1965). increase distance”,
  • Mijajlovic , B ., “Fixed points of mapping on the normed and reflexive spaces”, Kragujevac J . Math . ‎29 : 113-120 .) 2006( ,
  • Mizumoto , M . and Tanaka , J ., “Some properties of fuzzy numbers in : M . M . Gupta et al . Editors” , Advances Applications , North-Holland , New-York : 153- 164, (1979) . Set Theory and
  • Sadeqi , I . and Solaty kia , F ., “Some fixed point theorems in fuzzy reflexive Banach spaces” , Chaos , Solitons and Fractals , 41 : 2606-2612 (2009) .
  • Sadeqi , I ., Moradlou , F . and Salehi , M ., “On approximate cauchy equation in Felbin's type fuzzy normed linear spaces” , Iranian Journal of Fuzzy Systems , 10 (3) : 51-63, (2013).
  • Smulian , V .,“ On the principle of inclusion in the space of the type (B)”, Math . Sb . (N . S . ) , 5: 237-238 , (1939) .
  • Vajzovic , F . and Stefanovic , M ., “Two fixed point theorems”, Radovi Akad . Nauka Bosnei Herceg. , 24: 63-71, (1985) .
  • Xiao , J . and Zhu , X ., “On linearly topological structure and property of fuzzy normed linear space”, Fuzzy Sets and Systems, 125: 153-161, (2002).
There are 18 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Bayaz Daraby

Z. Solimani

Publication Date December 16, 2015
Published in Issue Year 2015 Volume: 28 Issue: 4

Cite

APA Daraby, B., & Solimani, Z. (2015). Fixed Points Of Mappings On The Fuzzy Reflexive Spaces. Gazi University Journal of Science, 28(4), 729-735.
AMA Daraby B, Solimani Z. Fixed Points Of Mappings On The Fuzzy Reflexive Spaces. Gazi University Journal of Science. December 2015;28(4):729-735.
Chicago Daraby, Bayaz, and Z. Solimani. “Fixed Points Of Mappings On The Fuzzy Reflexive Spaces”. Gazi University Journal of Science 28, no. 4 (December 2015): 729-35.
EndNote Daraby B, Solimani Z (December 1, 2015) Fixed Points Of Mappings On The Fuzzy Reflexive Spaces. Gazi University Journal of Science 28 4 729–735.
IEEE B. Daraby and Z. Solimani, “Fixed Points Of Mappings On The Fuzzy Reflexive Spaces”, Gazi University Journal of Science, vol. 28, no. 4, pp. 729–735, 2015.
ISNAD Daraby, Bayaz - Solimani, Z. “Fixed Points Of Mappings On The Fuzzy Reflexive Spaces”. Gazi University Journal of Science 28/4 (December 2015), 729-735.
JAMA Daraby B, Solimani Z. Fixed Points Of Mappings On The Fuzzy Reflexive Spaces. Gazi University Journal of Science. 2015;28:729–735.
MLA Daraby, Bayaz and Z. Solimani. “Fixed Points Of Mappings On The Fuzzy Reflexive Spaces”. Gazi University Journal of Science, vol. 28, no. 4, 2015, pp. 729-35.
Vancouver Daraby B, Solimani Z. Fixed Points Of Mappings On The Fuzzy Reflexive Spaces. Gazi University Journal of Science. 2015;28(4):729-35.