Common ï¬xed points for generalized ψ-contractions in weak non-Archimedean fuzzy metric spaces
Submitted: 2017-05-03
|Accepted: 2019-02-16
|Published: 2019-04-01
Downloads
Keywords:
common ï¬xed point, compatible mappings, fuzzy metric spaces, weak non-Achimedean fuzzy metric spaces, fuzzy topology, common limit
Supporting agencies:
Chiang Mai University
National Research Foundation of Korea (NRF)
Ministry of Science
ICT and future Planning (2014R1A2A2A01002100)
Thailand Research Fund and Office of the Higher Education Commission
Grant No. MRG6180050
Abstract:
Fixed point theory in fuzzy metric spaces plays very important role in theory of nonlinear problems in applied science. In this paper, we prove an existence result of common fixed point of four nonlinear mappings satisfying a new type of contractive condition in a generalized fuzzy metric space, called weak non-Archimedean fuzzy metric space. Our main results can be applied to solve the existence of solutions of non-linear equations in fuzzy metric spaces. Some examples supporting our main theorem are also given. Our results improve and generalize some recent results contained in Vetro (2011)[16]to generalized contractive conditions under some suitable conditions and many known results in the literature.
References:
Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math. 5 (1997), 949-962.
A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
A. George and P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems. 90 (1997), 365-368. https://doi.org/10.1016/S0165-0114(96)00207-2
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1989), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
M. Jain, K. Tas, S. Kumar and N. Gupta, Coupled fixed point theorems for a pair of weakly compatible maps along with CLRg-property in fuzzy metric spaces, J. Appl. Math. 2012 (2012) Art. ID 961210, 13 pp. https://doi.org/10.7763/ijapm.2012.v2.130
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), 771-779. https://doi.org/10.1155/S0161171286000935
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4 (1996), 19-215.
I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 336-344.
S. Manro and C. Vetro, Common fixed point theorems in fuzzy metric spaces employing CLRg and JCLRst properties, Ser. Math. Inform. 29 (2014), 77-90. https://doi.org/10.1155/2014/486102
J. Martínez-Moreno, A. Roldán, C. Roldán and Y. J. Cho, Multi-dimensional coincidence point theorems for weakly compatible mappings with the CLRg-property in (fuzzy) metric spaces, Fixed Point Theory Appl. 2015, 2015:53. https://doi.org/10.1186/s13663-015-0297-2
D. Mihet, Fuzzy ψ-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008), 739-744. https://doi.org/10.1016/j.fss.2007.07.006
A.-F. Roldán-López-de-Hierro and W. Sintunavarat, Common fixed point theorems in fuzzy metric spaces using the CLRg-property, Fuzzy Sets and Systems 282 (2016), 131-142. https://doi.org/10.1016/j.fss.2014.11.005
A. Sapena, A contribution to the study of fuzzy metric spaces, Applied General Topology 2, no. 1 (2001), 63-75. https://doi.org/10.4995/agt.2001.3016
B. Schweizer and A. Sklar, Statistical metric space, Pacific J. Math. 10 (1960), 314-334. https://doi.org/10.2140/pjm.1960.10.313
C. Vetro, Fixed points in weak non-Archimedean fuzzy metric spaces, Fuzzy Sets Syst. 162 (2011), 84-90. https://doi.org/10.1016/j.fss.2010.09.018
L. A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
