Fixed Point Theory for Decomposable Sets

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.

From the reviews:

"The book under review provides a thorough analysis of decomposable sets, the fixed point theory of maps on such sets, and applications of this theory. provides a comprehensive examination of the theory, starting with the background and preliminaries, going through the essence of the arguments of decomposability, and presenting a variety of applications. All in all the text is very useful to active researchers and to the general community including advanced students ." (Zvi Artstein, Mathematical Reviews, Issue 2005 k)

Inhalt
Preliminaries.- Real and vector measures.- Preliminary notions.- Upper and lower semicontinuous multifunctions.- Measurable multifunctions.- Carathéodory type multifunctions.- Fixed points property for convex-valued mappings.- Decomposable sets.- Selections.- Fixed points property.- Aumann integrals.- Selections of Aumann integrals.- Fixed points for multivalued contractions.- Operator and differential inclusions.- Decomposable analysis.