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Fixed point theory for Volterra Kakutani Monch maps

Banaś J., O'Regan D.

Journal of Mathematics and Applications

2008

Vol. 30

33-41

New fixed point theorems for multivalued Volterra Kakutani Mönch maps between Fréchet spaces are presented. The proof relies on fixed point theory in Banach spaces and viewing a Frechét space as the projective limit of a sequence of Banach spaces.

Set differential equations in Frechet spaces

Galanis G., N., Bhaskar T., G., Lakshmikantham V.

Journal of Applied Analysis

2008

Vol. 14, nr 1

103-113

It is known that a frachet space F can be realized as a projective limit of a sequence of Banach spaces Ei. The space Kc(F) of all compact, convex subsets of a Frechet space, F, is realized as a projective limit of the semilinear metric spaces Kc(Ei). Using the notion of Hukuhara derivative for maps with values in Kc(F), we prove the local and global existence theorems for an initial value problem associated with a set differential equation.

Fixed point theory for multimaps defined on closed subsets of Frechet spaces: the projective limit approach

Agarwal R.P., O'Regan D.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2006

Vol. 46, [Z] 2

169-179

New fixed point results are presented for maps defined on closed subsets of a Fr´echet space E. The proof relies on fixed point results in Banach spaces and viewing E as the projective limit of a sequence of Banach spaces.