Continuation theorems for weakly inward Kakutani and Strongly inward acyclic maps
Volume 15, Issue 3, pp 203--208
http://dx.doi.org/10.22436/jnsa.015.03.03
Publication Date: March 09, 2022
Submission Date: December 12, 2021
Revision Date: January 24, 2022
Accteptance Date: January 26, 2022
Authors
D. O'Regan
- School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland.
Abstract
In this paper we begin by presenting a general Leray-Schauder alternative and a
topological transversality theorem for Kakutani (upper semicontinuous maps with nonempty convex compact values) compact weakly inward maps. Then with some observations and extra assumptions we present a Leray-Schauder alternative and a
topological transversality theorem for acyclic (upper semicontinuous maps with nonempty acyclic compact values) compact strongly inward maps.
Share and Cite
ISRP Style
D. O'Regan, Continuation theorems for weakly inward Kakutani and Strongly inward acyclic maps, Journal of Nonlinear Sciences and Applications, 15 (2022), no. 3, 203--208
AMA Style
O'Regan D., Continuation theorems for weakly inward Kakutani and Strongly inward acyclic maps. J. Nonlinear Sci. Appl. (2022); 15(3):203--208
Chicago/Turabian Style
O'Regan, D.. "Continuation theorems for weakly inward Kakutani and Strongly inward acyclic maps." Journal of Nonlinear Sciences and Applications, 15, no. 3 (2022): 203--208
Keywords
- Essential maps
- homotopy
- inward maps
- acyclic maps
MSC
References
-
[1]
R. P. Agarwal, D. O'Regan, Fixed points for admissible multimaps, Dynam. Systems Appl., 11 (2002), 437--448
-
[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]
K. Deimling, Multivalued differential equations, Walter de Gruyter & Co., Berlin (1992)
-
[4]
P. M. Fitzpatrick, W. V. Petryshyn, Fixed point theorems for multivalued noncompact acyclic mappings, Pacific J. Math., 54 (1974), 17--23
-
[5]
G. Fournier, H.-O. Peitgen, On some fixed point principles for cones in linear normed spaces, Math. Ann., 225 (1977), 205--218
-
[6]
A. Granas, J. Dugundji, Fixed Point Theory, Springer-Verlag, New York (2003)
-
[7]
B. Halpern, Fixed point theorems for set--valued maps in infinite dimensional spaces, Math. Ann., 189 (1970), 87--98
-
[8]
D. O'Regan, A continuation theory for weakly inward maps, Glasgow Math. J., 40 (1998), 311--321
-
[9]
D. O'Regan, Homotopy and Leray--Schauder type results for admissible inward multimaps, J. Concr. Appl. Math., 2 (2004), 67--76
-
[10]
D. O'Regan, Continuation theorems for acyclic maps in topological spaces, Commun. Appl. Anal., 13 (2009), 39--46