Marlène Frigon

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In this paper, we present fixed point results for generalized contractions defined on a complete gauge space E. Also, we consider families of generalized contractions {f t : X → E} t∈[0,1] where X ⊂ E is closed and can have empty interior. We give conditions under which the existence of a fixed point for some f t 0 imply the existence of a fixed point for(More)
We establish fixed point theorems for multivalued mappings defined on a closed subset of a complete metric space. We generalize Lim's result on weakly inward contractions in a Banach space. We also generalize recent results of Azé and Corvellec, Maciejewski, and Uderzo for contractions and directional contractions. Finally, we present local fixed point(More)
New fixed point results are presented for admissible pairs and maps (admissible in the sense of Górniewicz) defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree theory, and on viewing E as the projective limit of a sequence of Banach spaces. A survey of recent fixed point theory in Fréchet spaces, Nonlinear(More)
Thèse présentée à la Faculté des études supérieures de l'Université de Montréal en vue de l'obtention du grade de Philosophiae Doctor (Ph.D.) en statistique et à l'Université Montpellier II en vue de l'obtention du grade de Docteur d'Université en Mathématiques appliquées et applications des mathématiques décembre 2002 Cette thèse de doctorat effectuée en(More)
In this paper, we introduce some aspects of a critical point theory for multivalued functions Φ : E → R N ∪{∞} defined on E a complete gauge space and with closed graph. The existence of a critical point is established in presence of linking. Finally, we present applications of this theory to semilinear elliptic problems on R N .
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