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A FIXED POINT THEOREM IN HILBERT C*-MODULES

  • Ranjbar, Hasan (Department of Mathematics, Mashhad Branch, Islamic Azad University) ;
  • Niknam, Asadollah (Department of Mathematics, Mashhad Branch, Islamic Azad University)
  • Received : 2021.07.10
  • Accepted : 2022.04.27
  • Published : 2022.06.30

Abstract

Fixed point theory has many useful applications in applied sciences. The object of this paper is to obtain fixed point for continuous self mappings in Hilbert C*-module with rational conditions.

Keywords

References

  1. Browder, F.E, Fixed point theorems for noncompact mappings in Hilbert spaces, Proc. Natl. Acad. Sci. USA. 43 (1965), 1272-1276. https://doi.org/10.1073/pnas.53.6.1272
  2. Browder, F.E, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sei. U.S.A. 54 (1965), 1041-1044. https://doi.org/10.1073/pnas.54.4.1041
  3. Fisher, B, A fixed point theorem for compact metric space, Publ. Inst. Math. 25 (1976),193-194.
  4. Gohde, D, Zum Prinzip der kontraktiven Abbildung, Math. Nachr. 30 (1965), 251-258. https://doi.org/10.1002/mana.19650300312
  5. Kannan, R, Some results on fixed point theorems, Bull. Calcutta. Math. Soc. 60 (1969), 71-78.
  6. Kaplansky, I, Modules over operator algebras, Amer. J. Math. 75 (4) (1953), 839-853. https://doi.org/10.2307/2372552
  7. Kirk, W.A, A fixed point theorem for mappings which do not increase distance, Amer. Math. Monthly. 72 (1965), 1004-1006. https://doi.org/10.2307/2313345
  8. Koparde, P.V. and Waghmode, B.B, Kannan type mappings in Hilbert spaces, Scientist Phyl. Sciences 3 (1) (1991), 45-50.
  9. Lance, E.C, Hilbert C*-modules, A toolkit for operator algebraists, Cambridge Univ. Press, Cambridge 1995.
  10. Phillips, N.C. and Weaver, N, Modules with norms which take values in a C*-algebra, Pacific J. of Maths, 185 (1) (1998), 163-181. https://doi.org/10.2140/pjm.1998.185.163
  11. Sharma, A.K., Badshah, V.H and Gupta, V.K, Common fixed point theorems in Hilbert space, International Academy of Sciences, Engg. And Tech. 3 (2014), 63-70.