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A fixed point theorem in Hilbert $C^*$-modules

Hasan Ranjbar|Asadollah Niknam
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2022.06|한국수학논문집 (Korean Journal of Mathematics)|제30권 제2호|pp. 297-304

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참고문헌

키워드

Fixed pointHilbert $C^*$-modulecontinuous self mapping
주제분류수학

초록

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.

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.

참고문헌 (11)

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

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