Locally admissible multi-valued maps
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 31 (2011) no. 1, pp. 115-132.

Voir la notice de l'article provenant de la source Library of Science

In this paper we generalize the class of admissible mappings as due by L. Górniewicz in 1976. Namely we define the notion of locally admissible mappings. Some properties and applications to the fixed point problem are presented.
Keywords: Lefschetz number, fixed point, absolute neighborhood multi-retracts, admissible maps, locally admissible maps
@article{DMDICO_2011_31_1_a5,
     author = {\'Slosarski, Miros{\l}aw},
     title = {Locally admissible multi-valued maps},
     journal = {Discussiones Mathematicae. Differential Inclusions, Control and Optimization},
     pages = {115--132},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2011},
     zbl = {1264.55003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMDICO_2011_31_1_a5/}
}
TY  - JOUR
AU  - Ślosarski, Mirosław
TI  - Locally admissible multi-valued maps
JO  - Discussiones Mathematicae. Differential Inclusions, Control and Optimization
PY  - 2011
SP  - 115
EP  - 132
VL  - 31
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMDICO_2011_31_1_a5/
LA  - en
ID  - DMDICO_2011_31_1_a5
ER  - 
%0 Journal Article
%A Ślosarski, Mirosław
%T Locally admissible multi-valued maps
%J Discussiones Mathematicae. Differential Inclusions, Control and Optimization
%D 2011
%P 115-132
%V 31
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMDICO_2011_31_1_a5/
%G en
%F DMDICO_2011_31_1_a5
Ślosarski, Mirosław. Locally admissible multi-valued maps. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 31 (2011) no. 1, pp. 115-132. http://geodesic.mathdoc.fr/item/DMDICO_2011_31_1_a5/

[1] G.P. Agarwal and D. O'Regan, A note on the Lefschetz fixed point theorem for admissible spaces, Bull. Korean Math. Soc. 42 (2) (2005), 307-313. doi: 10.4134/BKMS.2005.42.2.307

[2] J. Andres and L. Górniewicz, Topological principles for boundary value problems, Kluwer, 2003.

[3] S.A. Bogatyi, Approximative and fundamental retracts, Math. USSR Sb. 22 (1974), 91-103. doi: 10.1070/SM1974v022n01ABEH001687

[4] S. Eilenberg and D. Montomery, Fixed points theorems for multi-valued transformations, Amer. J. Math. 58 (1946), 214-222. doi: 10.2307/2371832

[5] L. Górniewicz, Topological methods in fixed point theory of multi-valued mappings, Springer, 2006.

[6] L. Górniewicz and D. Rozpłoch-Nowakowska, The Lefschetz fixed point theory for morphisms in topological vector spaces, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center 20 (2002), 315-333. doi: 10.7151/dmdico.1130

[7] L. Górniewicz and M. Ślosarski, Once more on the Lefschetz fixed point theorem, Bull. Polish Acad. Sci. Math. 55 (2007), 161-170.

[8] L. Górniewicz and M. Ślosarski, Fixed points of mappings in Klee admissible spaces, Control and Cybernetics 36 (3) (2007), 825-832. doi: 10.4064/ba55-2-7

[9] A. Granas, Generalizing the Hopf- Lefschetz fixed point theorem for non-compact ANR's, in: Symp. Inf. Dim. Topol., Baton-Rouge, 1967.

[10] A. Granas and J. Dugundji, Fixed Point Theory, Springer, 2003.

[11] J. Leray and J. Schauder, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup. 51 (1934).

[12] H.O. Peitgen, On the Lefschetz number for iterates of continuous mappings, Proc. AMS 54 (1976), 441-444.

[13] R. Skiba and M. Ślosarski, On a generalization of absolute neighborhood retracts, Topology and its Applications 156 (2009), 697-709. doi: 10.1016/j.topol.2008.09.007

[14] M. Ślosarski, On a generalization of approximative absolute neighborhood retracts, Fixed Point Theory 10 (2) (2009), 329-346.

[15] M. Ślosarski, Fixed points of multivalued mappings in Hausdorff topological spaces, Nonlinear Analysis Forum 13 (1) (2008), 39-48.