Geodesic
Generalized coincidence theory for set-valued maps
O'Regan, Donal1
1 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 3, p. 855-864.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This paper presents a coincidence theory for general classes of maps based on the notion of a $\Phi$-essential map (we will also discuss $\Phi$-epi maps).
DOI : 10.22436/jnsa.010.03.01
Classification : 47H04, 47H10, 54H25, 54M20
Keywords: Essential maps, epi maps, coincidence points, homotopy.

O'Regan, Donal 1

1 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland 
@article{JNSA_2017_10_3_a0,
     author = {O'Regan, Donal},
     title = {Generalized coincidence theory for set-valued maps},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {855-864},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2017},
     doi = {10.22436/jnsa.010.03.01},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.03.01/}
}
TY  - JOUR
AU  - O'Regan, Donal
TI  - Generalized coincidence theory for set-valued maps
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 855
EP  - 864
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.03.01/
DO  - 10.22436/jnsa.010.03.01
LA  - en
ID  - JNSA_2017_10_3_a0
ER  - 
%0 Journal Article
%A O'Regan, Donal
%T Generalized coincidence theory for set-valued maps
%J Journal of nonlinear sciences and its applications
%D 2017
%P 855-864
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.03.01/
%R 10.22436/jnsa.010.03.01
%G en
%F JNSA_2017_10_3_a0
O'Regan, Donal. Generalized coincidence theory for set-valued maps. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 3, p. 855-864. doi : 10.22436/jnsa.010.03.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.03.01/

[1] Agarwal, R. P.; O’Regan, D. Nonlinear essential maps of Mönch , 1-set contractive demicompact and monotone (S)+ type, J. Appl. Math. Stochastic Anal., Volume 14 (2001), pp. 293-301 | DOI

[2] Agarwal, R. P.; O’Regan, D. A note on the topological transversality theorem for acyclic maps, Appl. Math. Lett., Volume 18 (2005), pp. 17-22 | Zbl | DOI

[3] Browder, F. E. Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis, Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., (1968), 1–308, Amer. Math. Soc., Providence, R. I., 1976

[4] Browder, F. E. Fixed point theory and nonlinear problems , Bull. Amer. Math. Soc. (N.S.), Volume 9 (1983), pp. 1-39

[5] Furi, M.; Martelli, M.; Vignoli, A. On the solvability of nonlinear operator equations in normed spaces, Ann. Mat. Pura Appl., Volume 124 (1980), pp. 321-343 | DOI

[6] Gabor, G.; Górniewicz, L.; M. Ślosarski Generalized topological essentiality and coincidence points of multivalued maps, Set-Valued Var. Anal., Volume 17 (2009), pp. 1-19 | DOI | Zbl

[7] Granas, A. Sur la méthode de continuité de Poincaré , C. R. Acad. Sci. Paris Sr. A-B, Volume 282 (1976), pp. 983-985 | Zbl

[8] Kato, T. Demicontinuity, hemicontinuity and monotonicity , Bull. Amer. Math. Soc., Volume 70 (1964), pp. 548-550 | Zbl | DOI

[9] Kato, T. Demicontinuity, hemicontinuity and monotonicity, II , Bull. Amer. Math. Soc., Volume 73 (1967), pp. 886-889 | DOI | Zbl

[10] D. O’Regan Continuation methods based on essential and 0-epi maps, Acta Appl. Math., Volume 54 (1998), pp. 319-330 | Zbl | DOI

[11] O’Regan, D. Continuation theorems for acyclic maps in topological spaces, Commun. Appl. Anal., Volume 13 (2009), pp. 39-45 | Zbl

[12] O’Regan, D. Homotopy principles for d-essential acyclic maps, J. Nonlinear Convex Anal., Volume 14 (2013), pp. 415-422 | Zbl

[13] O’Regan, D. Coincidence points for multivalued maps based on \(\Phi\)-epi and \(\Phi\)-essential maps, Dynam. Systems Appl.,, Volume 24 (2015), pp. 143-154 | Zbl

[14] O’Regan, D.; Precup, R. Theorems of Leray-Schauder type and applications, Series in Mathematical Analysis and Applications,http://www.isr-publications.com/admin/jnsa/articles/3576/edit Gordon and Breach Science Publishers, Amsterdam, 2001

Cité par Sources :