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

• Autorzy: Agarwal R.P. , O'Regan D.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

fixed point theory; projective limits; Frechet space

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 2
• Strony: 169--179
• Opis fizyczny: bibliogr. 10 poz.

Twórcy

autor

Agarwal R.P.

autor

O'Regan D.

• Department of Mathematics, Florida Institute of Technology Melbourne, Florida 32901, USA

Bibliografia

• [1] R. P. Agarwal, M. Frigon and D. O'Regan, A survey of recent fixed point theory in Fréchet spaces, Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th birthday, Kluwer Acad. Publ., Dordrecht Vol. 1 (2003), 75-88.
• [2] R. P. Agarwal, M. Meehan and D. O'Regan, Fixed point theory and applications, Cambridge University Press, Cambridge, 2001.
• [3] R. P. Agarwal and D. O'Regan, Fixed point theory for admissible multimaps defined on closed subsets of Fréchet spaces, Jour. Math. Anal. Appl. 277 (2003), 438-445.
• [4] R. P. Agarwal and D. O'Regan, Multivalued nonlinear equations on the half line: a fixed point approach, Korean Jour. Computational and Applied Math. 9 (2002), 509-524.
• [5] M. Frigon, Fixed point results for compact maps on closed subsets of Fr´echet spaces and applications to differential and integral equations, Bull. Soc. Math. Belgique 9 (2002), 23-37.
• [6] M. Frigon and D. O'Regan, Fixed points of cone-compression and cone-expanding operators in Fréchet spaces, Bull. London Math. Soc. 35 (2003), 672-680.
• [7] L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, Pergamon Press, Oxford 1964.
• [8] V. Lakshmikantham and S. Leela, Differential and integral inequalities, Academic Press, New York, Vol. 1 1969.
• [9] D. O'Regan and M. Meehan, Existence theory for nonlinear integral andintegrodifferential equations, Kluwer Acad. Publishers, Dordrecht 1998.
• [10] D. O'Regan, Maximal solutions and multivalued differential and integral inclusions on a noncompact interval, Nonlinear Functional Analysis and Applications, 11 (2006), 335-342.