FIXED POINT THEOREMS IN d-COMPLETE TOPOLOGICAL SPACES

  • Received : 2009.10.12
  • Accepted : 2010.04.16
  • Published : 2010.05.30

Abstract

We prove the existence of common fixed points for three self mappings satisfying contractive conditions in d-complete topological spaces. Our results are generalizations of result of Troy L. Hicks and B. E. Roades[Troy L. Hicks and B. E. Roades, Fixed points for pairs of mappings in d-complete topological spaces, Int. J. Math. and Math. Sci., 16(2)(1993), 259-266].

Keywords

References

  1. R. P. Agarawl, D. O. O'Regan, N. Shahzad, Fixed point theorems for generalized contractive maps of Mei-Keeler type, Math. Nachr. 276 (2004), 3-12. https://doi.org/10.1002/mana.200310208
  2. J. P. Aubin, J. Siegel, Fixed point and stationary points of dissipative multi-valued maps, Proc. Amer. Math. Soc. 78 (1980), 391-398. https://doi.org/10.1090/S0002-9939-1980-0553382-1
  3. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 29 (2002), 531-536. https://doi.org/10.1155/S0161171202007524
  4. H. Covitz, S. B. Nadler Jr., Multi-valued contraction mappings in generalized metric spaces, Israel J. Math. 8 (1970), 5-11. https://doi.org/10.1007/BF02771543
  5. Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings and multivalued Caristi type mappings, J. Math. Anal. Appl. 317 (2006), 103-112. https://doi.org/10.1016/j.jmaa.2005.12.004
  6. Troy L. Hicks, Fixed point theorems for d-complete topological spaces I, Int. J. Math. and Math. Sci. 15 (1992), 435-440. https://doi.org/10.1155/S0161171292000589
  7. Troy L. Hicks and B. E. Roades, Fixed point theorems for d-complete topological spaces II, Math. Japonica 37 (1992), 847-853.
  8. Troy L. Hicks and B. E. Roades, Fixed points for pairs of mappings in d-complete topological spaces, Int. J. Math. and Math. Sci. 16(2) (1993), 259-266. https://doi.org/10.1155/S0161171293000304
  9. S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-478. https://doi.org/10.2140/pjm.1969.30.475
  10. P. Vijayaraju, B. E. Rhoades, R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contracive condition of integral type, Int. J. Math. Math. Sci. 15 (2005), 2359-2364.
  11. T. Wang, Fixed point theorems and fixed point stability for multivalued mappings on metric spaces, J. Nanjing Univ. Math. Baq. 6 (1989), 16-23.