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Zbl 0989.47046
Agarwal, Ravi P.; O'Regan, Donal
Cone compression and expansion fixed point theorems in Fréchet spaces with applications. (English)
[J] J. Differ. Equations 171, No.2, 412-429 (2001). ISSN 0022-0396

The authors present a new kind of fixed point theory for multivalued maps between Fréchet spaces. \par From the text: ``This paper is concerned with the existence of single and multiple fixed points for multivalued maps between Fréchet spaces. There are two main sections. In Section 2, the fixed point theory of Krasnosel'skij and Leggett and Williams and Petryshyn [see {\it R. P. Agarwal} and {\it Donal O'Regan} [J. Differ. Equations 160, No. 2, 389-403 (2000; Zbl 1008.47055); Nonlinear Anal., Theory Methods Appl. 42A, No. 6, 1091-1099 (2000; Zbl 0969.47038)] and their references) in Banach spaces are extended to the Fréchet space setting. Existence of fixed points will be established by means of a diagonal process together with a result on hemicompact maps [{\it K. K. Tan} and {\it X.-Z. Yuan}, J. Math. Anal. Appl. 185, No. 2, 378-390 (1994; Zbl 0856.47036)]. Section 3 shows how the fixed point theory in Section 2 can be applied naturally to obtain general existence results for nonlinear integral inclusions''.
[S.L.Singh (Rishikesh)]

MSC 2000:: *47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H04 Set-valued operators
47H09 Mappings defined by "shrinking" properties
47G20 Integro-differential operators
46A04 Locally convex Frechet spaces, etc.

Keywords: cone compression; expansion fixed point theorems; fixed point theory; multivalued maps between Fréchet spaces; diagonal process; hemicompact maps; nonlinear integral inclusions

Citations: Zbl 1008.47055; Zbl 0969.47038; Zbl 0856.47036

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