# Generalized coincidence theory for set-valued maps

Volume 10, Issue 3, pp 855--864 Publication Date: March 20, 2017       Article History
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### Authors

Donal O'Regan - School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland.

### Abstract

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).

### Keywords

• Essential maps
• epi maps
• coincidence points
• homotopy.

•  47H04
•  47H10
•  54H25
•  54M20

### References

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

• [2] R. P. Agarwal, D. O’Regan, A note on the topological transversality theorem for acyclic maps, Appl. Math. Lett., 18 (2005), 17–22.

• [3] F. E. Browder, 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] F. E. Browder, Fixed point theory and nonlinear problems , Bull. Amer. Math. Soc. (N.S.), 9 (1983), 1–39.

• [5] M. Furi, M. Martelli, A. Vignoli, On the solvability of nonlinear operator equations in normed spaces, Ann. Mat. Pura Appl., 124 (1980), 321–343.

• [6] G. Gabor, L. Górniewicz, M. Ślosarski , Generalized topological essentiality and coincidence points of multivalued maps, Set-Valued Var. Anal., 17 (2009), 1–19.

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

• [8] T. Kato, Demicontinuity, hemicontinuity and monotonicity , Bull. Amer. Math. Soc., 70 (1964), 548–550.

• [9] T. Kato, Demicontinuity, hemicontinuity and monotonicity, II , Bull. Amer. Math. Soc., 73 (1967), 886–889.

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

• [11] D. O’Regan, Continuation theorems for acyclic maps in topological spaces, Commun. Appl. Anal., 13 (2009), 39–45.

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

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

• [14] D. O’Regan, R. Precup, 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)