IJPAM: Volume 120, No. 3 (2018)

Title

ON COMMON FIXED POINT THEOREMS FOR
MULTIVALUED MAPPINGS IN INTUITIONISTIC
FUZZY METRIC SPACE

Authors

Rajinder Sharma$^1$, Deepti Thakur$^2$
$^1$Sohar College of Applied Sciences
Mathematics Section, OMAN
$^2$Sohar College of Applied Sciences
Mathematics Section, OMAN

Abstract

This study deals with some common fixed point theorems for multi-valued mappings in intuitionistic fuzzy metric space by relaxing the condition of continuous mapping and replacing the completeness of the space with a set of an alternative conditions. We improve some earlier results.

History

Received: November 13, 2016
Revised: January 2, 2019
Published: January 3, 2019

AMS Classification, Key Words

AMS Subject Classification: 47H10, 54H25
Key Words and Phrases: common fixed point, multi-valued mappings, weak compatible maps, intuitionistic fuzzy metric space

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96.

2
Alaca, C., Turkoglu and Yildiz, C., Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solit. and Fract., 29 (2006), 1073-1078.

3
Banach, S., Surles operations dansles ensembles abstracts at leur applications aux equations integrals,Fund. Math., 3 (1922), 133-181.

4
Cho, Y.J., Fixed Point in fuzzy metric spaces, J. Fuzzy Math., 5(4) (1997), 949- 962.

5
Cho, Y.J., Pathak, H.K.,Kang, S.M. and Jung, J.S., Common fixed points of compatible maps of type $(\alpha)$ on fuzzy metric spaces,Fuzzy sets and systems, 93(1998), 99-111.

6
Ciric, L.B., Fixed Point for generalized multivalued contractions, Math. Vesnik, 9(24) (1972), 99-11.

7
Grabiec, M., Fixed point in fuzzy metric spaces, Fuzzy sets and Systems, 27 (1988), 385- 389.

8
George, A. and Veermani,P., On some results in fuzzy metric spaces, Fuzzy sets and Systems, 64 (1994), 385-399.

9
George, A. and Veermani,P., On some results of analysis for fuzzy metric spaces, Fuzzy sets and Systems , 90 (1997), 365- 368.

10
Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83(1976),261- 263.

11
Jungck, G., Compatible mappings and common fixed points (2), Internat. J. Math. and Math. Sci., 11(1988),285-288.

12
Jungck, G., Murthy,P.P. and Cho, Y.J., Compatible mappings of type (A) and common fixed points , Math. Japon., 38(2)(1993), 381-390.

13
Jungck, G. and Rhoades, B.E., Fixed points for set valued functions without continuity, Ind. J. Pure and Appl. Maths., 29 (3)(1998), 227-238.

14
Kramosil,I. and Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetika, 11, 1975, 326-334.

15
Kubiaczyk, I. and Sharma, S., Common coincidence point in fuzzy metric space, J. Fuzzy Math., 11(1) (2003), 1-5.

16
Kubiaczyk, I. and Sharma, S., Common fixed point , multi-maps in fuzzy metric space, East Asian Math. J., 18(2) (2002), 175-182.

17
Mishra, S.N., Sharma N., and Singh, S.L., Common fixed points of maps in fuzzy metric spaces, Internat. J. Math. and Math. Sci., 17 (1994), 253-258.

18
Park, J.H., Intuitionistic fuzzy metric spaces, Chaos, Solit. and Fract., 22 (2004),1039-1046.

19
Sharma, S. , Common Fixed Point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 127 (2002), 345-352.

20
Sessa, S., On weak commutativity condition of mappings in a fixed point considerations, Pub. Inst. Math.,32 (46) (1982),149-153.

21
Sharma, S., Servet, K. and Rathore, R.S. , Common Fixed Point for multivalued mappings in intutionistic fuzzy metric space, Comm. Kor. Math. Soc., 22(3)(2007), 391-399.

22
Turkoglu, D., Alaca C., and Yildiz C., Compatible maps and compatible maps of type $(\alpha)$ and $(\beta)$ in intuitionistic fuzzy metric spaces, Demons. Math.,39(3) (2006),671-684.

23
Turkoglu, D., Alaca C , Cho, Y. J. ,and Yildiz,C., Common fixed point theorems intuitionistic fuzzy metric spaces, J. Appl. Math. Computing 22 (1-2) (2006), 411-424.

24
Schweizer, B. and Skaler, A., Statistical metric spaces, Pac. J. Math.,10 (1960), 313-334.

25
Zadeh, L.A., Fuzzy Sets, Infor. and Control, 8 (1965), 338-353.

How to Cite?

DOI: 10.12732/ijpam.v120i3.13 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 120
Issue: 3
Pages: 447 - 459


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).