On local and global injectivity of noncompact vector fields in non necessarily locally convex vector spaces

Holger Alex

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 239-248
  • ISSN: 0010-2628

Abstract

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We give in this paper conditions for a mapping to be globally injective in a topological vector space.

How to cite

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Alex, Holger. "On local and global injectivity of noncompact vector fields in non necessarily locally convex vector spaces." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 239-248. <http://eudml.org/doc/247624>.

@article{Alex1994,
abstract = {We give in this paper conditions for a mapping to be globally injective in a topological vector space.},
author = {Alex, Holger},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {fixed point index; locally injective mappings; $(\varphi , \gamma )$-condensing mappings; local injectivity; topological vector space; relative fixed point index for compactly reducible maps},
language = {eng},
number = {2},
pages = {239-248},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On local and global injectivity of noncompact vector fields in non necessarily locally convex vector spaces},
url = {http://eudml.org/doc/247624},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Alex, Holger
TI - On local and global injectivity of noncompact vector fields in non necessarily locally convex vector spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 239
EP - 248
AB - We give in this paper conditions for a mapping to be globally injective in a topological vector space.
LA - eng
KW - fixed point index; locally injective mappings; $(\varphi , \gamma )$-condensing mappings; local injectivity; topological vector space; relative fixed point index for compactly reducible maps
UR - http://eudml.org/doc/247624
ER -

References

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  1. Alex H., Hahn S., Kaniok L., The fixed point index for noncompact mappings in non locally convex topological vector spaces, Comment. Math. Univ. Carolinae 35 (1994), 249-257. (1994) Zbl0807.47038MR1286571
  2. Alex H., Hahn S., On the uniqueness of the fixed point in the Schauder fixed point theorem, Radovi Mathematicki 6 (1990), 265-271. (1990) Zbl0724.47031MR1096708
  3. Banach S., Mazur S., Über mehrdeutige stetige Abbildungen, Studia Math. 5 (1934), 174-178. (1934) 
  4. Deimling K., Nonlinear Functional Analysis, Springer Verlag, Berlin-Heidelberg-New YorkTokyo, 1985. Zbl0559.47040MR0787404
  5. Hadzic O., Fixed Point Theory in Topological Vector Spaces, Novi Sad, 1984. Zbl0576.47030MR0789224
  6. Hadzic O., Some properties of measures of noncompactness in paranormed spaces, Proc. Amer. Math. Soc. 102 (1988), 843-849. (1988) Zbl0653.47034MR0934854
  7. Hahn S., Gebietsinvarianzsatz und Eigenwertaussagen für konzentrierende Abbildungen, Comment. Math. Univ. Carolinae 18 (1977), 697-713. (1977) Zbl0375.47029MR0474385
  8. Hahn S., Homöomorphieaussagen für k -verdichtende Vektorfelder, Comment. Math. Univ. Carolinae 21 (1980), 563-572. (1980) Zbl0452.47061MR0590135
  9. Hahn S., Fixpunktsätze für limeskompakte Abbildungen in nicht notwendig lokalkonvexen topologischen Vektorräumen, Comment. Math. Univ. Carolinae 27 (1986), 189-204. (1986) MR0843430
  10. Kaniok L., On measures of noncompactness in general topological vector spaces, Comment. Math. Univ. Carolinae 31 (1990), 479-487. (1990) Zbl0738.47051MR1078482
  11. Kellogg R.B, Uniqueness in the Schauder fixed point theorem, Proc. Amer. Math. Soc. 60 (1976), 207-210. (1976) MR0423137
  12. Plastock R., Homeomorphisms between Banach spaces, Trans. Amer. Math. Soc. 200 (1974), 169-183. (1974) Zbl0291.54009MR0356122
  13. Riedrich T., Vorlesungen über nichtlineare Operatorengleichungen, Teubner-Texte zur Mathematik, Leipzig, 1976. Zbl0332.47026MR0467414
  14. Rinow W., Lehrbuch der Topologie, Berlin, 1975. Zbl0317.54001MR0514884
  15. Smith H.L., Stuart C.A., A uniqueness theorem for fixed points, Proc. Amer. Math. Soc. 79 (1980), 237-240. (1980) Zbl0438.47055MR0565346
  16. Talmann L.A., A note on Kellogg's uniqueness theorem for fixed points, Proc. Amer. Math. Soc. 69 (1978), 248-250. (1978) MR0467416

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