Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

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

Abstrakty

EN

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

Słowa kluczowe

EN

multivalued maps; Fréchet space; degree and index theory; projective limit

Kategorie tematyczne

• 47H11: Degree theory
• 47H10: Fixed-point theorems

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2007
• Tom: 27
• Numer: 2
• Strony: 399-409

Daty

wydano

2007

otrzymano

2007-02-15

Twórcy

autor

R.P. Agarwal

• Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901, USA

autor

D. O'Regan

• Department of Mathematics, National University of Ireland, Galway, Ireland

autor

D.R. Sahu

• Department of Applied Mathematics, Shri Shankaracharya College of Engineering & Technology, Junwani, Bhilai-490020, India

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 1 (2003), 75-88.
• [2] R.P. Agarwal and D. O'Regan, An index theory for countably P-concentrative J maps, Applied Math. Letters 16 (2003), 1265-1271.
• [3] J. Andres, G. Gabor and L. Gorniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc. 351 (1999), 4861-4903.
• [4] P.M. Fitzpatrick and W.V. Petryshyn, Fixed point theorems and fixed point index for multivalued mappings in cones, J. London Math. Soc. 12 (1975), 75-82.
• [5] L. Gorniewicz, A. Granas and W. Kryszewski, On the homotopy method in the fixed point index theory of multi-valued mappings of compact absolute neighborhood retracts, J. Math. Anal. Appl. 161 (1991), 457-473.
• [6] L.V. Kantorovich and G.P. Akilov, Functional analysis in normed spaces, Pergamon Press, Oxford, 1964.
• [7] D. O'Regan, Y.J. Cho and Y.Q. Chen, Topological Degree Theory and Applications, Chapman and Hall/CRC, Boca Raton, 2006.
• [8] M. Väth, Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal. 13 (1999), 341-363.
• [9] M. Väth, Merging of degree and index theory, Fixed Point Theory and Applications, Volume 2006 (2006), Article ID 36361, 30 pages.

Identyfikatory

DOI

10.7151/dmdico.1092