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Existence, uniqueness and approximation of fixed points as a generic property

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References

  1. A. Alexiewicz andW. Orlicz, Some remarks on the existence and uniquess of solutions of the hyperbolic equation\(\frac{{\partial ^2 }}{{\partial x\partial y}}z = f(x,y,z,\frac{\partial }{{\partial x}}z,\frac{\partial }{{\partial y}}z),\) Studia Math.15 (1956), 201–215.

    MATH  MathSciNet  Google Scholar 

  2. L. P. Belluce andW. A. Kirk,Fixed-Point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc.20 (1969, 141–146.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. E. Browder,Convergence of approximantes to fixed points of nonexpansive nonlinear mappings in Banach spaces, Arch. Rat. Mech. Anal.24 (1967), 82–90.

    Article  MATH  MathSciNet  Google Scholar 

  4. F. Cafiero,Sul fenomeno di Peano nelle equazioni differenziali ordinarie del primo ordine, Rend. Accad. Sci. Fis. Mat. Napoli17 (1950), 51–61, and II, 123–126.

    MathSciNet  Google Scholar 

  5. F. Cafiero,Sulla classe delle equazioni differenziali ordinarie del primo ordine, i cui punti dí Peano constituiscono um insieme di misura lebesguiana nulla, Rend. Accad. Sci. Fis. Mat. Napoli17 (1950), 127–137.

    MathSciNet  Google Scholar 

  6. G. Darbo,Punti uniti in transformazioni a codominio non Compatto, Rend. Sem. Mat. Univ. Padova24 (1955), 84–92.

    MathSciNet  Google Scholar 

  7. J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.

    MATH  Google Scholar 

  8. A. Lasota andJ. A. Yorke,The generic property of existence of solutions of differential equations in Banach space, J. Diff. Eqs.13 (1973), 1–12.

    Article  MATH  MathSciNet  Google Scholar 

  9. W. Orlicz,Zur Theorie der Differentialgleichung y′=f(x,y), Bull. Acad. Polon. Sci. (1932), 221–228.

  10. W. V. Petryshyn,Structure of the fixed points sets of k-set-contractions, Arch. Rat. Mech. Anal.40 (1971), 312–328.

    Article  MATH  MathSciNet  Google Scholar 

  11. Sadovskii,Limit-compact and condensing operators, Russ. Math. Surveys (1972).

  12. G. Vidossich,Approximation of fixed points of compact mappings, J. Math. Anal. Appl.34 (1971), 86–89.

    Article  MATH  MathSciNet  Google Scholar 

  13. G. Vidossich,Applications of Topology to Analysis: On the topological properties of the set of fixed points of nonlinear operators, Confer. Sem. Mat. Bari126 (1971), 1–62.

    Google Scholar 

  14. G. Vidossich,Existence, comparison and asymptotic behavior of solutions of ordinary differential equations in finite and infinite dimensional Banach spaces, submited.

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Authors and Affiliations

  1. Universidade de Brasilia, Brasilia, Brasil

    Giovanni Vidossich

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  1. Giovanni Vidossich
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Additional information

Parts of this research were made while the author was at Scuola Normale Superiore, Pisa, Italy, and the University of Cape Town, Rondebosch, South Africa.

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Vidossich, G. Existence, uniqueness and approximation of fixed points as a generic property. Bol. Soc. Bras. Mat 5, 17–29 (1974). https://doi.org/10.1007/BF02584769

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  • DOI: https://doi.org/10.1007/BF02584769

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