A generalization of the interior mapping theorem of Clarke and Pourciau

Marián J. Fabián; David Preiss

Commentationes Mathematicae Universitatis Carolinae (1987)

  • Volume: 028, Issue: 2, page 311-324
  • ISSN: 0010-2628

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Fabián, Marián J., and Preiss, David. "A generalization of the interior mapping theorem of Clarke and Pourciau." Commentationes Mathematicae Universitatis Carolinae 028.2 (1987): 311-324. <http://eudml.org/doc/17546>.

@article{Fabián1987,
author = {Fabián, Marián J., Preiss, David},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {interior mapping theorem; reflexive Banach spaces; locally approximable by convex subsets of linear continuous surjections; Caristi's fixed point principle},
language = {eng},
number = {2},
pages = {311-324},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A generalization of the interior mapping theorem of Clarke and Pourciau},
url = {http://eudml.org/doc/17546},
volume = {028},
year = {1987},
}

TY - JOUR
AU - Fabián, Marián J.
AU - Preiss, David
TI - A generalization of the interior mapping theorem of Clarke and Pourciau
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1987
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 028
IS - 2
SP - 311
EP - 324
LA - eng
KW - interior mapping theorem; reflexive Banach spaces; locally approximable by convex subsets of linear continuous surjections; Caristi's fixed point principle
UR - http://eudml.org/doc/17546
ER -

References

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  1. J. CARISTI, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251. (1976) Zbl0305.47029MR0394329
  2. F. H. CLARKE, On the inverse function theorem, Pacific J. Math. 64 (1976), 97-102. (1976) Zbl0331.26013MR0425047
  3. W. J. CRAMER, Jr. W. O. RAY, Solvability of nonlinear operator equations, Pacific J. Math. 95 (1981), 37-50. (1981) MR0631657
  4. J. DIESTEL, Geometry of Banach spaces - Selected topics, Lect. Notes 485, Springer Verlag, Berlin 1975. (1975) Zbl0307.46009MR0461094
  5. D. DOWNING W. A. KIRK, A generalization of Caristi's theorem with applications to nonlinear mapping theory, Pacific J. Math. 69 (1977), 339-346. (1977) MR0440426
  6. D. S. DŽUMABAEV, On solvability of nonlinear closed operator equations, (Russian), Izv. Akad. Nauk Kazach. SSR, Ser. Fyz.-Mat. No. 1, 1984, 31-34. (1984) MR0749322
  7. M. FABIAN, Concerning interior mapping theorem, Comment. Math. Univ. Carolinae 20 (1979), 345-356. (1979) Zbl0393.46008MR0539563
  8. M. FABIAN L. ZAJÍČEK V. ZIZLER, On residuality of the set of rotund norms on a Banach space, Math. Ann. 258 (1982), 349-351. (1982) MR0649205
  9. L. M. GRAVES, Some mapping theorems, Duke Math. J. 17 (1950), 111-114. (1950) Zbl0037.20401MR0035398
  10. V. PTÁK, A quantitative refinement of the closed graph theorem, Czech. Math. 3. 24 (1974), 503-506. (1974) MR0348431
  11. B. H. POURCIAU, Analysis and optimization of Lipschitz continuous mappings, J. Opt. Theory Appl. 22 (1977), 311-351. (1977) Zbl0336.26008MR0454813
  12. T. SZILÁGYI, Generalization of the implicit function theorem and of Banach s open mapping theorem, Acta Scient. Math. 38 (1977), 391-396. (1977) MR0501071
  13. C. URSESCU, [unknown], Letter to the first named author, January 1984. (1984) 

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