Pacific Journal of Mathematics

Fixed point theorems for multivalued noncompact acyclic mappings.

P. M. Fitzpatrick and W. V. Petryshyn

Article information

Source
Pacific J. Math., Volume 54, Number 2 (1974), 17-23.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102911290

Mathematical Reviews number (MathSciNet)
MR0405179

Zentralblatt MATH identifier
0312.47047

Subjects
Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Citation

Fitzpatrick, P. M.; Petryshyn, W. V. Fixed point theorems for multivalued noncompact acyclic mappings. Pacific J. Math. 54 (1974), no. 2, 17--23. https://projecteuclid.org/euclid.pjm/1102911290


Export citation

References

  • [1] F. E. Browder, The fixed point theory of multivalued mappings in topological vector spaces, Math. Annalen, 177 (1968), 283-301.
  • [2] E. W. Cheney and A. A. Goldstein, Proximity mapsfor convex sets, Proc. Amer. Math. Soc, 10 (1959), 448-450.
  • [3] J. Dugundji, An extension ofTietze's Theorem, Pacific J. Math., 1 (1951), 353-367.
  • [4] S. Eilenbergand D.Montgomery, Fixed point theoremsfor multivalued transformationsy Amer. J. Math., 68 (1946), 214-222.
  • [5] Ky Fan,Extensions of Wo fixed point theorems ofF. E. Browder, Math. Z., 112(1969), 234-240.
  • [6] I.T. Gohberg, L. S. Goldenstein and A. S. Markus, Investigations of some properties of bounded linear operators with their q-norms, Uch. Zap.Kishinevsk. In-ta., 29 (1957), 29-36.
  • [7] L. Grniewicz and A. Granas, Fixed point theorems for multivalued mappings of the absolute neighborhood retracts, J. Math. Pures et Appl., 49 (1970), 381-395.
  • [8] B. Halpern, Fixed point theorems for set-valued maps in infinite dimensional spaces, Math. Annalen, 189 (1970), 87-98.
  • [9] B.Halpern and G.Bergman, A fixedpoint theoremfor inward and outward maps, Trans. Amer. Math. Soc, 130 (1968), 353-358.
  • [10] S. T. Hu, Theory of Retracts, Wayne State Univ. Press,1965.
  • [11] C.Kuratowski,Sur les espaces complets, Fund. Math., 15 (1930), 301-309.
  • [12] T. W. Ma, Topological degree of set-valued compact vector fields in locally convex spaces, Dissertationes Math., 92 (1972), 1-43.
  • [13] R. D.Nussbaum, The fixed point indexfor local condensing maps, Annalidi Mat. Pura et Appl., 89 (1971), 217-258.
  • [14] W. V. Petryshyn, Fixed point theorem for various classes of 1-set-contractive and I-ball-contractive mappings in Banach spaces, Trans. Amer. Math. Scoc, 182 (1973), 323-352.
  • [15] W. V. Petryshyn and P. M. Fitzpatrick, A degree theory, fixed point theorems, and mapping theorems for multivalued noncompact mappings, Trans. Amer. Math. Soc., 194 (1974), 1-25.
  • [16] W. V. Petryshyn and P. M. Fitzpatrick, Fixed point theorems for multivalued noncompact inward mappings, J. Math. Anal, andAppl.,46 (1974), 756-767.
  • [17] M. J. Powers,Multivalued mappings and Lefschetz fixed point theorems, Proc. Camb. Phil. Soc,68 (1970), 619-630.
  • [18] S. Reich, Fixed points in locally convex spaces, Math. Z.,125 (1972), 17-31.
  • [19] B. N. Sadovsky, Ultimately compact and condensing mappings, Uspehi Mat. Nauk, 27 (1972), 81-146.
  • [20] T. Van der Walt, Fixed and almost fixed points, Math. Center Tracts, No. 1,128pp., Amsterdam, 1963.