Surveys in Mathematics and its Applications


ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 5 (2010), 265 -- 273

COMMON FIXED POINT THEOREM FOR HYBRID PAIRS OF R-WEAKLY COMMUTING MAPPINGS

R. K. Saini, Sanjeev Kumar and Peer Mohammed

Abstract. In this paper we established a common fixed point theorem for four mappings f,g (crisp) and S,T (fuzzy) of R -- weakly commuting mapping in a metric space.

2010 Mathematics Subject Classification: 54H25; 47H10; 03E72.
Keywords: Fixed Point Theorems; Weakly Commuting Fuzzy Maps; Contractive Conditions of Integral Type.

Full text

References

  1. S. C. Arora and V. Sharma, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 110 (2000), 127-130. MR1748116 Zbl 0988.54047.

  2. R. K. Bose and D. Sahani, Fuzzy mappings and fixed point theorems, Fuzzy Sets and Systems, 21 (1987), 53-58. MR0868355 (87m:54018). Zbl 0609.54032.

  3. D. Butnariu, Fixed points for fuzzy mappings, Fuzzy Sets and Systems, 7 (1982), 191 - 207. MR0644207 Zbl 0473.90087.

  4. S. S. Chang, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 17 (1985), 181 - 187. MR0811539 Zbl 0579.54034.

  5. A. Chitra, A note on the fixed point of fuzzy maps on partially ordered topological spaces, Fuzzy Sets and Systems, 19 (1986), 305 - 308. MR0848669 Zbl 0601.54058.

  6. S. Heilpern, Fuzzy mappings and fixed point theorem, J. Math. Anal. Appl., 83 (1981), 566-569. MR0641351 (83a:54070). Zbl 0486.54006.

  7. T. Kamran, Common coincidence points of R-weakly commuting map, IJMMS, 3 (2001), 179-182. MR1841104. Zbl 1006.54061.

  8. T. Kamran, Non-commuting f-contraction mappings, NOVI SAD J. Math., 34 No. 1, 2004, 33-37. MR2140186. Zbl 1085.54029.

  9. B. S. Lee and S. J. Cho, A fixed point theorem for contractive type fuzzy mappings, Fuzzy Sets and Systems, 61 (1994), 309-312. MR1273252. Zbl 0831.54036 .

  10. S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488. MR0254828. Zbl 0187.45002.

  11. H. K. Pathak, Y. J. Cho, and S. M. Kang, Common fixed points of biased maps of type (A) and applications, Internat. J. Math. Math. Sci. 21 (1998), 681-694. MR1642200. Zbl 0920.47051.

  12. H. K. Pathak, Y. J. Cho, and S. M. Kang, Remarks on R-weakely commuting mappings and common fixed point theorems, Bull. Korean Math.Soc. 34(2) (1997) 247-257. MR1455445. Zbl 0878.54032.

  13. Padaliya, and R. P. Pant, Common fixed point theorem for R-weakly commuting mappings of type (Af), Soochow Journal of Mathematics, 31 No. 2 (2005), 155-163. MR2149868. Zbl 1071.54502.

  14. R. A. Rashwan and M. A. Ahmed, Common fixed point theorems for fuzzy mappings, Arch. Math. (Brno), 38 (2002), 219-226. MR1921593. Zbl 1068.54008.

  15. T. Som, R. N. Mukherjee, Some Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems, 33 (1989), 213-219. MR1024224. Zbl 0685.54030.

  16. M. D. Weiss, Fixed points, separation and induced fuzzy topologies for fuzzy sets mappings, J. Math. Anal. Appl. 50 (1975), 142 - 150. MR0370460. Zbl 0297.54004.

  17. L. A. Zadeh, Fuzzy sets, Inform and Control, 8 (1965), 338 - 353. MR0219427. Zbl 139.24606.



R. K. Saini Sanjeev Kumar
Department of Mathematics, Department of Mathematics,
D.A.V. College, D.A.V. College,
Muzzafernager-251001, UP, India. Muzzafernager-251001, UP, India.
e-mail:rksaini03@yahoo.com

Peer Mohammad
Department of Mathematics,
Eritrea Institute of Techonology, Asmara,
Eritrea.


http://www.utgjiu.ro/math/sma