International Journal of Nonlinear Analysis and Applications

Approximation properties in fuzzy cone normed linear space

Document Type : Research Paper

Authors

1 Department of Mathematics, Surya Sen Mahavidyalaya, Siliguri-734004, India

2 Department of Mathematics, Visva-Bharati, Santiniketan-731235, India

Abstract

The main purpose of this paper is to consider the best approximation in fuzzy cone normed linear space and study its related results. We introduce quotient fuzzy cone normed linear space and proved some results of approximation in such spaces. We also discuss the relation in proximity and Chebyshevity of a given space and its quotient space.

Keywords

[1] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), no. 3,
687–705.
[2] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, Ann. Fuzzy Math. Inf. 6 (2013), no 2,
271–283.
[3] S.C. Cheng and J.N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc.
86 (1994), no. 5, 429–436.
[4] K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, Germany, 1985.
[5] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets Syst. 48 (1992), 239–248.
[6] M. Goudarzi and S.M. Vaezpour, Best simultaneous approximatıon in fuzzy normed spaces, Iran. J. Fuzzy Syst.
7 (2010), no. 3, 87–96.
[7] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst. 12 (1984), 215–229.
[8] A.K. Katsaras, Fuzzy topological vector spaces, Fuzzy Sets Syst. 12 (1984), 143–154.
[9] George J. Klir and B. O. Yuan, Fuzzy Sets and Fuzzy Logic, Printice-Hall of India Private 353 Limited, New
Delhi, 1997.
[10] I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–334.
[11] H. Long-Guang, Z. Xian, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal.
Appl. 332 (2007) 1468-1476.
[12] R. Saadati and S.M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput. 17 (2005), 475-484.[13] P. Tamang and T. Bag, Some results on finite dimensional fuzzy cone normed linear space, Ann. Fuzzy Math.
Inf. 13 (2017), no. 1, 123–134.
[14] P. Tamang and T. Bag, Some fixed point results in fuzzy cone normed linear space, J. Egypt. Math. Soc. 27
(2019), 46.
[15] S.M. Vaezpour and F. Karimi, t-best approximation in fuzzy normed spaces, Iran. J. Fuzzy Syst. 5 (2008), No. 2,
93–99.
[16] L.A. Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338–353.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 2551-2563
  • Receive Date: 21 February 2021
  • Revise Date: 08 June 2021
  • Accept Date: 12 June 2021