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Tytuł artykułu

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

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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.
Twórcy
autor
  • Department of Mathematical Science, Florida Institute of Technology, Melbourne, Florida 32901, USA
autor
  • Department of Mathematics, National University of Ireland, Galway, Ireland
autor
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1092
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