# 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

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topR.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

top- [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. Zbl1063.47057
- [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] 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. Zbl0757.54019
- [6] L.V. Kantorovich and G.P. Akilov, Functional analysis in normed spaces, Pergamon Press, Oxford, 1964. Zbl0127.06104
- [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. Zbl0964.47025
- [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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