Abstract
The aim of this lecture is to present a new compactness method for operator inclusions in general, and for Hammerstein like inclusions, in particular. This method applies to acyclic multivalued maps which satisfy a generalized compactness condition of Monch type.
Authors
Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Multivalued map; acyclic map; Hammerstein operator; operator inclusion; compactness; fixed point.
Paper coordinates
R. Precup, Fixed point theorems for acyclic multivalued maps and inclusions of Hammerstein type, Seminar on Fixed Point Theory Cluj-Napoca, 3 (2002), 327-334.
About this paper
Journal
Seminar on Fixed Point Theory Cluj-Napoca, Volume 3, 2002, 327-334
Publisher Name
University ”Babeș-Bolyai”, Cluj-Napoca, Romania
DOI
Print ISSN
Online ISSN
MR 1929778, Zbl 1043.47037.
google scholar link
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[6] D. O’Regan and R. Precup, Fixed point theorems for set-valued maps and existence principles for integral inclusions, J. Math. Anal. Appl. 245 (2000), 594-612.
[7] D. O’Regan and R. Precup, Theorems of Leray-Schauder Type and Applications, Gordon and Breach Science Publishers, 2001.
[8] D. O’Regan and R. Precup, Integrable solutions of Hammerstein integral inclusions in Banach spaces, Dynam. Contin. Discrete Impuls. Systems, to appear.
[9] R. Precup, A Monch type generalization of the Eilenberg-Montgomery fixed point theorem, Seminar on Fixed Point Theory Cluj-Napoca 1 (2000), 69-71.
[10] R. Precup, On the Palais-Smale condition for Hammerstein integral equations, Nonlinear Anal. 47, no 2 (2001), 1233-1244.
[11] R. Precup, Inequalities and compactness, to appear