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Geometric fixed point theory and inwardness conditions

  • James Caristi
  • William A. Kirk
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 490)

Keywords

Banach Space Closed Subset Fixed Point Theorem Nonexpansive Mapping Contraction Mapping 
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References

  1. [1]
    N.A. Assad and W.A. Kirk, Fixed point theorems for set valued mappings of contractive type, Pacific J. Math. 43 (1972), 553–562.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    H. Brezis, On a characterization of flow invariant sets, Comm. Pure Appl. Math. 23 (1970), 261–263.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions.Google Scholar
  4. [4]
    B. Halpern, Fixed point theorems for outward maps, Doctoral Thesis, U.C.L.A. (1965).Google Scholar
  5. [5]
    B. Halpern and G. Bergman, A fixed point theorem for inward and outward maps, Trans. Amer. Math. Soc. 130 (1968), 353–358.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    R.H. Martin, Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc. 179 (1973), 399–414.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    W.V. Petryshyn and P.M. Fitzpatrick, Fixed point theorems for multivalued noncompact inward maps.Google Scholar
  8. [8]
    S. Reich, Remarks on fixed points, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 52 (1972), 690–697.MathSciNetzbMATHGoogle Scholar
  9. [9]
    S. Reich, Fixed points of condensing functions, J. Math. Anal. Appl. 41 (1973), 460–467.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    S. Reich, Fixed points of nonexpansive functions, J. London Math. Soc. 7 (1973), 5–10.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    G. Vidossich, Nonexistence of periodic solutions of differential equations and applications to zeros of nonlinear operators.Google Scholar
  12. [12]
    G. Vidossich, Applications of topology to analysis: On the topological properties of the set of fixed points of nonlinear operators, Confer. Sem. Mat. Univ. Bari 126 (1971), 1–62.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • James Caristi
    • 1
  • William A. Kirk
    • 1
  1. 1.The University of IowaUSA

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