A contractive mappings on fuzzy normed linear spaces

Document Type : Research Article

Author

• M. Saheli

Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

10.22067/ijnao.v6i1.41683

Abstract

‎In this paper‎, ‎we use the definition of fuzzy normed spaces given by Bag and Samanta and provide four types of fuzzy versions of contraction‎. ‎We show that these mappings necessarily have unique fixed points in fuzzy normed linear spaces‎. ‎We will show that the presented theorems are indeed fuzzy extensions of their classical counterparts‎.

Keywords

• Fuzzy norm
• Fuzzy normed linear space
• Fixed point
• α- seminorm
• Contractive conditions

20.1001.1.24236977.2016.6.1.7.9

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References

1. AL-Mayahi, N.F. and Hadi, S.H. On α-π-φ contraction in fuzzy metricspace and its application, General Mathematics Notes 26 (2) (2015), 104-118.

2. Bag, T. and Samanta, S.K. Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (3) (2003), 687-705.

3. Bag, T. and Samanta, S.K. Fuzzy bounded linear operators, Fuzzy Sets and Systems 151 (2005), 513-547.

4. Choudhury, B.S. Unique fixed point theorem for weakly c-contractive mappings, Kathmandu University Journal of Science, Engineering and Technology 5 (2009), 6-13.

5. Das, N.R. and Saha, M.L. On fixed points in fuzzy metric spaces, Annals of Fuzzy Mathematics and Informatics 7 (2) (2014), 313-318.

6. Kadelburg, Z. and Radenovic, S. On generalized metric spaces: a survey, TWMS J. Pure Appl. Math. 5 (1) (2014), 3-13.

7. Khan, M.S., Swaleh, M. and Sessa, S. Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30 (1) (1984), 1-9.

8. Manro, S. and Tomar, A. Faintly compatible maps and existence of common fixed points in fuzzy metric space, Annals of Fuzzy Mathematics and Informatics 8 (2) (2014), 223-230.

9. Rhoades, B.E. Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Applications 47 (4) (2001), 2683-2693.

10. Rosa, V.L. and Vetro, P. Common fixed points for α- -φ-contractions in generalized metric spaces, Nonlinear Analysis: Modelling and Control 19(1) (2014), 43-54.

11. Shukla, S. and Chauhan, S. Fuzzy cyclic contraction and fixed point theorems, Journal of the Egyptian Mathematical Society 23 (1) (2015), 139-143.