Fixed point results for $\mathscr{H}$-contractions in fuzzy metric spaces via admissible
Downloads
DOI:
https://doi.org/10.26637/MJM0603/0020Abstract
In the present work, we come out with the introduction of $\alpha-\psi$ - fuzzy $\mathscr{H}$ - contraction mapping in the setting of fuzzy metric spaces. We establish fixed point results for such contraction mappings in a complete fuzzy metric space. An example is bestowed to illustrate the applicability of the obtained result.
Keywords:
fuzzy metric space, t-norm, α - admissible, fuzzy H - contractive mappingMathematics Subject Classification:
Mathematics- Pages: 588-594
- Date Published: 01-07-2018
- Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)
I. Beg, D. Gopal, T. Došenović, D. Rakić $alpha$ - Type Fuzzy $mathscr{H}$ - Contractive Mappings in Fuzzy Metric Spaces, Fixed Point Theory, 19(2) (2018) 463-474.
A. George, P. Veeramani, On Some Results in Fuzzy Metric Spaces, Fuzzy Sets Syst., 64 (1994) 395 - 399.
D. Gopal and C. Vetro, Some New Fixed Point Theorems in Fuzzy Metric Spaces, Iranian Journal of Fuzzy Systems, 11(3) (2014) 95 - 107.
M. Grabiec, Fixed Points in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 27 (1988) 385-389.
V. Gregori, J. J. Miñana, Some Remarks on Fuzzy Contractive Mappings, Fuzzy Sets and Systems, 251 (2014) $101-103$.
V. Gregori, S. Morillas and A. Sapena, Examples of Fuzzy Metrics and Applications, Fuzzy Sets and Systems, 170 (2011) 95-111.
V. Gregori, A. Sapena, On Fixed Point Theorems in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 125 (2002) 245252.
I. Kramosil, J. Michalek, Fuzzy Metric and Statistical Metric Spaces, Kybernetica, 15 (1975) 326 - 334.
D. Mihet, A Banach Contraction Theorem in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 144 (2004) 431 439.
D. Mihet, On Fuzzy Contractive Mappings in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 158 (2007), 915 921.
D. Mihet, Fuzzy $psi$ - Contractive Mappings in NonArchimedean Fuzzy Metric Spaces, Fuzzy Sets and Systems, 159 (2008), 739 - 744.
D. Mihet, Erratum to Fuzzy $psi$ - Contractive Mappings in Non - Archimedean Fuzzy Metric Spaces Revisited [Fuzzy Sets and Systems, 159 (2008), 739-744], Fuzzy Sets and Systems, 161 (2010), 1150-1151.
D. Mihet, A Class of Contractions in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 161 (2010), 1131 - 1137.
D. Mihet, A Note on Fuzzy Contractive Mappings in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 251 (2014) $83-91$.
S.N. Mishra, Nilima Sharma, S. L. Singh, Common Fixed Points of Maps on Fuzzy Metric Spaces, Internat. J. Math. Math. Sci., 17(2) (1994) 253 - 258.
R. K. Saini, B. Singh and A. Jain, A fixed point theorem with implicit relation in fuzzy metric space, International Mathematical Forum, $5(50)$ (2010) 2485-2496.
S. Satish, Fuzzy $mathscr{H}$ - weak contractions and fixed point theorems in fuzzy metric spaces, Gulf Journal of Mathematics, 1(2) (2013) 171-179.
B. Schweizer, A. Sklar, Statistical Metric Spaces, Pacific J. Math., 10 (1960) 313 - 334.
R. Vasuki and P. Veeramani, Fixed Point Theorems and Cauchy Sequences in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 135 (2003), 415-417.
S. Wang, Answers to Some Open Questions on Fuzzy $psi$-Contractions in Fuzzy Metric Spaces, Fuzzy Sets and Systems, 222 (2013) 115-119.
D. Wardowski, Fuzzy Contractive Mappings and Fixed Points in Fuzzy Metric Space, Fuzzy Sets and Systems, 222 (2013) 108-114.
L.A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965) 338 353.
Similar Articles
- D. Rajan, A. Beulah, Characterization of fuzzy number fuzzy measure using fuzzy integral , Malaya Journal of Matematik: Vol. 6 No. 03 (2018): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.