# COINCIDENCES AND FIXED POINT THEOREMS FOR MAPPINGS SATISFYING CONTRACTIVE CONDITION OF INTEGRAL TYPE ON d-COMPLETE TOPOLOGICAL SPACES

• Published : 2012.10.31

#### Abstract

In this paper, we prove some fixed point theorems for some weaker forms of compatibility satisfying a contractive condition of integral type on d-complete Hausdorff topological spaces. Our results extend and generalize some well known previous results.

#### References

1. M. A. Ahmed, Common fixed point theorems for weakly compatible mappings, Rocky Mountain J. Math. 33 (2003), no. 4, 1189-1203. https://doi.org/10.1216/rmjm/1181075457
2. M. Altman, An integral test for series and generalized contractions, Amer. Math. Monthly 82 (1975), no. 8, 827-829. https://doi.org/10.2307/2319801
3. I. Altun and D. Turkoglu, A fixed point theorem on general topological spaces with a ${\tau}$-distance, Indian J. Math. 50 (2008), no. 1, 219-228.
4. I. Altun and D. Turkoglu, Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanese J. Math. 13 (2009), no. 4, 1291-1304. https://doi.org/10.11650/twjm/1500405509
5. I. Altun and D. Turkoglu, Some fixed point theorems for mappings satisfying contractive condition of integral type on d-complete topological spaces, Fasc. Math. 42 (2009), 5-15.
6. I. Altun, D. Turkoglu, and B. E. Rhoades, Fixed points of weakly compatible maps satisfying a general contractive condition of integral type, Fixed Point Theory Appl. 2007 (2007), Article ID 17301, 9 pages, doi:10.1155/2007/17301. https://doi.org/10.1155/2007/17301
7. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), no. 9, 531-536. https://doi.org/10.1155/S0161171202007524
8. R. Chugh and S. Kumar, Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. Math. Sci. 111 (2001), no. 2, 241-247. https://doi.org/10.1007/BF02829594
9. Lj. B. Ciric and J. S. Ume, Some common fixed point theorems for weakly compatible mappings, J. Math. Anal. Appl. 314 (2006), no. 2, 488-499. https://doi.org/10.1016/j.jmaa.2005.04.007
10. T. L. Hicks and B. E. Rhoades, Fixed point theorems for d-complete topological spaces II, Math. Japon. 37 (1992), no. 5, 847-853.
11. K. Iseki, An approach to fixed point theorems, Math. Sem. Notes Kobe Univ. 3 (1975), no. 2, 193-202.
12. G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), no. 4, 261-263. https://doi.org/10.2307/2318216
13. G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779. https://doi.org/10.1155/S0161171286000935
14. G. Jungck, Compatible mappings and common fixed points. II, Internat. J. Math. Math. Sci. 11 (1988), no. 2, 285-288. https://doi.org/10.1155/S0161171288000341
15. G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.
16. H. Kaneko and S. Sessa, Fixed point theorems for compatible multi-valued and single- valued mappings, Internat. J. Math. Math. Sci. 12 (1989), no. 2, 257-262. https://doi.org/10.1155/S0161171289000293
17. S. Kasahara, On some generalizations of Banach contraction theorem, Math. Sem. Notes Kobe Univ. 3 (1975), no. 2, paper no. XXIII, 10 pp.
18. S. Kasahara, Some fixed point and coincidence theorems in L-spaces, Math. Sem. Notes Kobe Univ. 3 (1975), no. 2, paper no. XXVIII, 7 pp.
19. S. Kasahara, Fixed point iterations in L-space, Math. Sem. Notes Kobe Univ. 4 (1976), 205-210.
20. J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc. 62 (1977), no. 2, 344-348. https://doi.org/10.1090/S0002-9939-1977-0436113-5
21. V. Popa, A general fixed point theorem for four weakly compatible mappings satisfying an implicit relation, Filomat 19 (2005), 45-51.
22. B. E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2003 (2003), no. 63, 4007-4013. https://doi.org/10.1155/S0161171203208024
23. B. E. Rhoades and S. Sessa, Common fixed point theorems for three mappings under a weak commutativity condition, Indian J. Pure Appl. Math. 17 (1986), no. 1, 47-57.
24. S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), no. 46, 149-153.
25. S. Sessa and B. Fisher, Common fixed points of weakly commuting mappings, Bull. Polish Acad. Sci. Math. 35 (1987), no. 5-6, 341-349.
26. S. L. Singh, K. S. Ha, and Y. J. Cho, Coincidence and fixed points of nonlinear hybrid contractions, Internat. J. Math. Math. Sci. 12 (1989), no. 2, 247-256. https://doi.org/10.1155/S0161171289000281
27. S. L. Singh and S. N. Mishra, Remarks on Jachymski's fixed point theorems for com- patible maps, Indian J. Pure Appl. Math. 28 (1997), no. 5, 611-615.
28. D. Turkoglu and I. Altun, A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying an implicit relation, Bol. Soc. Mat. Mexicana (3) 13 (2007), no. 1, 195-205.
29. D. Turkoglu, I. Altun, and B. Fisher, Fixed point theorem for sequences of maps, Demon- stratio Math. 38 (2005), no. 2, 461-468.
30. P. Vijayaraju, B. E. Rhoades, and R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2005 (2005), no. 15, 2359-2364. https://doi.org/10.1155/IJMMS.2005.2359