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

R.P. Agarwal; D. O'Regan; D.R. Sahu

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 2, page 399-409
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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R.P. Agarwal, D. O'Regan, and D.R. Sahu. "Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.2 (2007): 399-409. <http://eudml.org/doc/271195>.

@article{R2007,
abstract = {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.},
author = {R.P. Agarwal, D. O'Regan, D.R. Sahu},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {multivalued maps; Fréchet space; degree and index theory; projective limit; fixed point theorems},
language = {eng},
number = {2},
pages = {399-409},
title = {Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory},
url = {http://eudml.org/doc/271195},
volume = {27},
year = {2007},
}

TY - JOUR
AU - R.P. Agarwal
AU - D. O'Regan
AU - D.R. Sahu
TI - Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 2
SP - 399
EP - 409
AB - 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.
LA - eng
KW - multivalued maps; Fréchet space; degree and index theory; projective limit; fixed point theorems
UR - http://eudml.org/doc/271195
ER -

References

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  1. [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. [2] R.P. Agarwal and D. O'Regan, An index theory for countably P-concentrative J maps, Applied Math. Letters 16 (2003), 1265-1271. Zbl1063.47057
  3. [3] J. Andres, G. Gabor and L. Gorniewicz, Boundary value problems on infinite intervals, Trans. Amer. Math. Soc. 351 (1999), 4861-4903. Zbl0936.34023
  4. [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. [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. Zbl0757.54019
  6. [6] L.V. Kantorovich and G.P. Akilov, Functional analysis in normed spaces, Pergamon Press, Oxford, 1964. Zbl0127.06104
  7. [7] D. O'Regan, Y.J. Cho and Y.Q. Chen, Topological Degree Theory and Applications, Chapman and Hall/CRC, Boca Raton, 2006. 
  8. [8] M. Väth, Fixed point theorems and fixed point index for countably condensing maps, Topol. Methods Nonlinear Anal. 13 (1999), 341-363. Zbl0964.47025
  9. [9] M. Väth, Merging of degree and index theory, Fixed Point Theory and Applications, Volume 2006 (2006), Article ID 36361, 30 pages. 

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