COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS

Year 2008, Volume: 37 Issue: 2, 97 - 106, 01.02.2008

K. P. R. Rao G. R. Babu B. Fisher

https://izlik.org/JA83ZN72EZ

Abstract

COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS

https://izlik.org/JA83ZN72EZ

Abstract

In this paper we introduce the notion of a pair (f, g) being weakly fcompatible and obtain a common fixed point theorem for self maps in fuzzy metric spaces which modifies and generalizes some known results. We also give a common fixed point theorem for self maps in sequentially compact fuzzy metric spaces.

Keywords

Sequentially compact , Common fixed points

References

• Banach, S. Theoric les operations Lineairar (Manograic Mathematic Zne, Warsaw, 1932).
• Cho, Seong Hoon On common fixed points in fuzzy metric spaces, International Mathemat- ical Forum 1 (10), 471–479, 2006.
• Cho, Y. J., Pathak, H, K., Kang, S. M. and Jung, J. S. Common fixed points of compatible maps of type (β) on fuzzy metric spaces, Fuzzy Sets and Systems, 93, 99–111, 1998.
• Edelstein, M. On fixed and periodic points under contradiction mapping, J. London Math. Soc. 37, 74–79, 1962.
• Fang, J.X. On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 46, –113, 1992.
• Fisher, B. Results on common fixed points on bounded metric spaces, Math. Sem. Notes 7, –80, 1979.
• George, A. and Veeramani, P. On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64, 395–399, 1994.
• Grabiec, M. Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27, 385–389, 1988.
• Jungck, G. and Rhoades, B. E. Fixed points for set-valued functions without continuity, Indian J. Pure. Appl. Math., 29 (3), 227–238, 1998.
• Khan, M. S., Pathak, H. K. and George, R. Compatible mapping of type (A-1) and type (A-2) and common fixed points in fuzzy metric spaces, International Mathematical Forum (11), 515–524, 2007.
• Kramosil, O. and Michalek, J. Fuzzy metric and statistical metric spaces, Kybernetica 11, –334, 1975.
• Lopez, J. Rodrigues and Romaguera, S. The Hausdorff fuzzy metric on compact sets, Fuzzy Sets and Systems 147 (2), 273–283, 2004.
• Mishra, S. N., Sharma, S. N. and Singh, S. L. Common fixed points of maps in fuzzy metric spaces, Internat. J. Math. Sci. 17, 253–258, 1994.
• Naidu, S. V. R. Fixed point theorems for four self maps on a metric space by altering dis- tance, J. Indian Math. Soc., 71 (1-4), 153–173, 2004.
• Schweizer, B. and Sklar, A. Statistical metric spaces, Pacific J. Math. 10, 314–334, 1960.
• Sharma, S. Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, , 345–352, 2002.
• Singh, Bijenra and Chauhan, M. S. Common fixed points of compatible maps in fuzzy metric spaces, Fuzzy Sets and Systems 115, 471–475, 2000.
• Zadeh, L. A. Fuzzy sets, Inform. and Control, 8, 338–353, 1965.