Some Fixed Point Theorems in φ-ψ weak contraction on Fuzzy Metric Space

R. Krishnakumar¹ , K. Dinesh² , D. Dhamodharan³

1. Department of Mathematics,Urumu Dhanalakshmi College, Tiruchirappalli, India.
2. Department of Mathematics,Urumu Dhanalakshmi College, Tiruchirappalli, India.
3. Department of Mathematics,Jamal Mohamed College (Autonomous),Tiruchirappalli, India.

Correspondence should be addressed to: dinesh.skksv93@gmail.com.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.3 , pp.146-152, Jun-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.146152

Online published on Jun 30, 2018

Copyright © R. Krishnakumar, K. Dinesh, D. Dhamodharan . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

391 Views    136 Downloads    104 Downloads

Abstract :
In this paper, we discuss some results on fixed point theorems in φ-ψ weak contraction on fuzzy metric spaces, which are study of generalisation of some existing results are also given in the form of corollary.

Key-Words / Index Term :
fuzzy metric space, continuous t-norm, φ-ψ weak contraction

References :
[1] C. T. Aage, Binayak S. Choudhury and Krishnapada Das, Some fixed point results in fuzzy metric spaces using control function, Surveys in Mathematics and its Applications, 12 (2017), 23 -34.
[2] K.Amit, and K.V Ramesh, Common fixed point theorem in fuzzy metric space using control function, Commun. Korean Math. Soc. 28 (2013), 517-526.
[3] Arslan Hojat Ansari, R. Krishnakumar and D.Dhamodharan, Common Fixed Point of Four Mapping with Contractive Modulus on Cone Banach Space via cone C-class function, Global Journal of Pure and Applied Mathematics, 13(9) (2017), 5593–5610.
[4] D.Dhamodharan and R. Krishnakumar, Cone S-Metric Space and Fixed Point Theorems of Contractive mappings, Annals of Pure and Applied Mathematics, 14(2)(2017), 237-243.
[5] A.George, and P.Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399.
[6] A.George, and P.Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365-399.
[7] M.Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389.
[8] V.Gregori, Samuel Morillas, and Almanzor Sapena, Examples of fuzzy metrics and applications, Fuzzy Sets and Systems, 170 (2011), 95-111.
[9] Hsien-Chung Wu, Common Coincidence Points and Common Fixed Points in Fuzzy Semi-Metric Spaces, Mathematics, 6 (29), (2018), 1-21
[10] Humaira, Muhammad Sarwar, and G. N. V. Kishore, Fuzzy Fixed Point Results For ϕ Contractive Mapping with
Applications, Hindawi Complexity,2018, (2018) 12 pages,doi.org/10.1155/2018/5303815
[11] M.S.Khan, M.Swaleh and S.Sessa, Fixed point theorems by altering distance between the points, Bull. Aust. Math. Soc.,
30(1984), 1-9.
[12] J.Kramosil, and J.Michalek, Fuzzy metric and Statistical metric spaces, Kybernetica, 11 (1975), 326-334.
[13] R.Krishnakumar, K. Dinesh, Fixed Point Theorems of Fuzzy Function in Complete Metric Spaces , International Journal
Of Innovative Research In Science, Engineering And Technology, 6(7), (2017), 13557-13562
[14] R. Krishnakumar, K. Dinesh, Fuzzy Mapping and their Fixed Point Theorems in Complete Metric Spaces, International Journal of Scientific Research in Science, Engineering and Technology, 3(8) (2017), 241-249
[15] B.Schweizer, and A.Sklar, Statistical metric spaces, Pacific Journal of Mathematics, 10 (1960), 313-334.
[16] Y.Shen, Dong Qiu and Wei Chen, Fixed point theorems in fuzzy metric spaces, Applied mathematics Letters, 25 (2012),
138-141
[17] Krishnadhan Sarkar, Kalishankar Tiwary, “Common Fixed Point Theorems for Wealkly Compatible mapping on Cone Banach Space” IJSRMSS, Volume 5, issu-2,pp-75-79 (April 2018)
[18] L.A.Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.