Author	Fryszkowski, Andrzej. author
Title	Fixed Point Theory for Decomposable Sets [electronic resource] / by Andrzej Fryszkowski
Imprint	Dordrecht : Springer Netherlands : Imprint: Springer, 2004
Connect to	http://dx.doi.org/10.1007/1-4020-2499-1
Descript	XI, 209 p. online resource

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

Preliminaries -- Real and vector measures -- Preliminary notions -- Upper and lower semicontinuous multifunctions -- Measurable multifunctions -- Carathรฉodory 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

1. Mathematics
2. Functional analysis
3. Measure theory
4. Differential equations
5. Convex geometry
6. Discrete geometry
7. Calculus of variations
8. Mathematics
9. Functional Analysis
10. Convex and Discrete Geometry
11. Measure and Integration
12. Ordinary Differential Equations
13. Calculus of Variations and Optimal Control; Optimization