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COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS

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

Abstract

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.

COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS

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

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.

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.
There are 18 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Mathematics
Authors

K. P. R. Rao This is me

G. R. Babu This is me

B. Fisher This is me

Publication Date February 1, 2008
Published in Issue Year 2008 Volume: 37 Issue: 2

Cite

APA Rao, K. P. R., Babu, G. R., & Fisher, B. (2008). COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS. Hacettepe Journal of Mathematics and Statistics, 37(2), 97-106.
AMA Rao KPR, Babu GR, Fisher B. COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS. Hacettepe Journal of Mathematics and Statistics. February 2008;37(2):97-106.
Chicago Rao, K. P. R., G. R. Babu, and B. Fisher. “COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS”. Hacettepe Journal of Mathematics and Statistics 37, no. 2 (February 2008): 97-106.
EndNote Rao KPR, Babu GR, Fisher B (February 1, 2008) COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS. Hacettepe Journal of Mathematics and Statistics 37 2 97–106.
IEEE K. P. R. Rao, G. R. Babu, and B. Fisher, “COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS”, Hacettepe Journal of Mathematics and Statistics, vol. 37, no. 2, pp. 97–106, 2008.
ISNAD Rao, K. P. R. et al. “COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS”. Hacettepe Journal of Mathematics and Statistics 37/2 (February 2008), 97-106.
JAMA Rao KPR, Babu GR, Fisher B. COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS. Hacettepe Journal of Mathematics and Statistics. 2008;37:97–106.
MLA Rao, K. P. R. et al. “COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS”. Hacettepe Journal of Mathematics and Statistics, vol. 37, no. 2, 2008, pp. 97-106.
Vancouver Rao KPR, Babu GR, Fisher B. COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES UNDER IMPLICIT RELATIONS. Hacettepe Journal of Mathematics and Statistics. 2008;37(2):97-106.