Decomposable sets since T. R. Rockafellar in 1968 are one of basic notions in nonlinear analysis, especially in the theory of multifunctions. A subset K of measurable functions is called decomposable if
(Q) for all and measurable A.
This book attempts to show the present stage of "decomposable analysis" from the point of view of fixed point theory. The book is split into three parts, beginning with the background of functional analysis, proceeding to the theory of multifunctions and lastly, the decomposability property.
Mathematicians and students working in functional, convex and nonlinear analysis, differential inclusions and optimal control should find this book of interest. A good background in fixed point theory is assumed as is a background in topology.
Author(s): Andrzej Fryszkowski (auth.)
Series: Topological Fixed Point Theory and Its Applications 2
Edition: 1
Publisher: Springer Netherlands
Year: 2004
Language: English
Pages: 209
City: Dordrecht; Boston
Tags: Functional Analysis; Convex and Discrete Geometry; Measure and Integration; Ordinary Differential Equations; Calculus of Variations and Optimal Control; Optimization
Preliminaries....Pages 3-21
Real and vector measures....Pages 23-53
Preliminary notions....Pages 57-58
Upper and lower semicontinuous multifunctions....Pages 59-79
Measurable multifunctions....Pages 81-92
Carathéodory type multifunctions....Pages 93-105
Fixed points property for convex-valued mappings....Pages 107-111
Decomposable sets....Pages 115-125
Selections....Pages 127-138
Fixed points property....Pages 139-140
Aumann integrals....Pages 141-151
Selections of Aumann integrals....Pages 153-162
Fixed points for multivalued contractions....Pages 163-170
Operator and differential inclusions....Pages 171-184
Decomposable analysis....Pages 185-198
