Fixed point theorems for acyclic multivalued maps and inclusions of Hammerstein type

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.

PDF

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

[1] J.-F. Couchouron and R. Precup, Existence principles for inclusions of Hammerstein type involving noncompact acyclic multivalued maps, to appear.
[2] S. Eilenberg and D. Montgomery, Fixed point theorems for multivalued transformations, Amer. J. Math. 68 (1946), 214-222.
[3] D. Guo, V. Lakshmikantham and X. Liu, Nonlinear Integral Equations in Abstract Spaces, Kluwer Academic Publishers, Dordrecht, 1996.
[4] S. Hu and N. S. Papageorgiou, Handbook of Multivalued Analysis, Vol. I: Theory, Kluwer Academic Publishers, Dordrecht-Boston-London, 1997.
[5] H. Monch, Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces, Nonlinear Anal. 4 (1980), 985-999.
[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

2002

Related Posts