Mathematische Annalen

, Volume 192, Issue 2, pp 155–172 | Cite as

Surjectivity theorems for odd maps ofA-proper type

  • W. V. Petryshyn


Surjectivity Theorem 
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  1. 1.
    Asplund, E.: Averaged norms. Israel J. Math.5, 227–233 (1967).Google Scholar
  2. 2.
    Borsuk, K.: Drei Sätze über dien-dimensionale Euklidische Sphäre. Fund. Math.21, 177–190 (1933).Google Scholar
  3. 3.
    Brezis, H.: Equations et inequations non lineaires dans les espaces vectoriels en dualite. Ann. de L'Institut Fourier, De L'Univ. de Grenoble, TomeXVIII (1), 115–175 (1968).Google Scholar
  4. 4.
    Browder, F. E.: Nonlinear eigenvalue problems and Galerkin approximations. Bull. Amer. Math. Soc.74, 651–656 (1968).Google Scholar
  5. 5.
    -- Nonlinear operators and nonlinear equations of evelution in Banach spaces. Proc. Symp. Pure Math.18, Part 2, Amer. Math. Soc. Providence, R. I. (to appear).Google Scholar
  6. 6.
    —— Nonlinear elliptic boundary value problems and the generalized topological degree. Bull. Amer. Math. Soc.76, 999–1005 (1970).Google Scholar
  7. 7.
    —— DeFigueiredo, D. G.:J-monotone nonlinear operators in Banach spaces. Kongl. Nederl. Akad. Wetesch.69, 412–418 (1966).Google Scholar
  8. 8.
    —— Petryshyn, W. V.: The topological degree and Galerkin approximations for noncompact operators in Banach spaces. Bull. Amer. Math. Soc.74, 641–646 (1968).Google Scholar
  9. 9.
    ———— Approximation methods and the generalized topological degree for nonlinear mappings in Banach spaces. J. Functional Anal.3, 217–245 (1969).Google Scholar
  10. 10.
    Calvert, B. D.: The local fixed point index for multivalued transformations (to appear).Google Scholar
  11. 11.
    Deimling, K.: Fixed points of generalizedP-compact operators. Math. Z.115, 188–196 (1970).Google Scholar
  12. 12.
    Fan, K., Glickberg, I.: Some geometric properties of the sphere in a normed linear space. Duke Math. J.25, 533–568 (1958).Google Scholar
  13. 13.
    Fitzpatrick, P. M.: A generalized degree for uniform limits ofA-proper mappings. J. Math. Anal. Appl. (to appear).Google Scholar
  14. 14.
    Kadec, M. I.: Spaces isomorphic to a locally uniformly convex space. Izv. Vyshch. Ucheb. Zaved. Matematika13, 51–57 (1959).Google Scholar
  15. 15.
    Kato, T.: Demicontinuity, hemicontinuity and monotonitity. II. Bull. Amer. Math. Soc.73, 886–889 (1967).Google Scholar
  16. 16.
    Nussbaum, R. D.: The fixed point index and fixed point theorems fork-set-contractions. Univ. of Chicago, Ph. D. Thesis, 1969.Google Scholar
  17. 17.
    Petryshyn, W. V.: On the approximation-solvability of nonlinear functional equations in normed linear spaces. Num. Anal. of PDE (Ed. J. L. Lions), C.I.M.E., Italy, 1967.Google Scholar
  18. 18.
    —— On the approximation-solvability of nonlinear equations. Math. Ann.177, 156–164 (1968).Google Scholar
  19. 19.
    —— On the projectional-solvability and Fredholm Alternative for equations involving linearA-proper operators. Archive Rat. Mech. Anal.30, 270–284 (1968).Google Scholar
  20. 20.
    —— Fixed point theorems involvingP-compact, semicontractive, and accretive operators not defined on all of a Banach space. J. Math. Anal. Appl.23, 336–354 (1968).Google Scholar
  21. 21.
    —— Invariance of domain theorem for locallyA-proper mappings and its implications. J. Functional Anal.5, 137–159 (1970).Google Scholar
  22. 22.
    —— On existence theorems for nonlinear equations involving noncompact mappings. Proc. National Acad. Sci. USA67, 326–330 (1970).Google Scholar
  23. 23.
    Petryshyn, W. V.: On nonlinear equations involving pseudo-A-proper mappings and their uniform limits with applications (to appear).Google Scholar
  24. 24.
    —— A characterization of strict convexity of Banach spaces and other uses of duality mappings. J. Functional Analysis6, 282–291 (1970).Google Scholar
  25. 25.
    —— Antipodes theorem forA-proper mappings and its applications to mappings of the modified type (S) or (S) and to mappings with thepm-property. J. Functional Anal.7, 165–211 (1971).Google Scholar
  26. 26.
    -- Nonlinear equations involving noncompact operators. Proc. Symp. Pure Math.18, Part 1, Amer. Math. Soc. Providence, R.I., 1970, 206–233.Google Scholar
  27. 27.
    —— Projection methods in nonlinear numerical functional analysis. J. Math. Mech.17, 353–372 (1967).Google Scholar
  28. 28.
    Pokhodjayev, S. I.: The solvability of nonlinear equations with odd operators. Functional Anal. i Prilozen.1, 66–73 (1967).Google Scholar
  29. 29.
    Taylor, A. E.: Introduction to functional analysis. New York: John Wiley and Sons, Inc. 1958.Google Scholar
  30. 30.
    Wong-Ng, Ship-Fah: Le degré topologique de certaines applications non-compactès, non-lineaires. Univ. of Montreal Ph. Thesis, 1969.Google Scholar

Copyright information

© Springer-Verlag 1971

Authors and Affiliations

  • W. V. Petryshyn
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

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