This textbook is devoted to a compressed and self-contained exposition of two important parts
of contemporary mathematics: convex and set-valued analysis. In the first part properties of
convex sets the theory of separation convex functions and their differentiability properties
of convex cones in finite- and infinite-dimensional spaces are discussed. The second part
covers some important parts of set-valued analysis. There the properties of the Hausdorff
metric and various continuity concepts of set-valued maps are considered. The great attention
is paid also to measurable set-valued functions continuous Lipschitz and some special types
of selections fixed point and coincidence theorems covering set-valued maps topological
degree theory and differential inclusions. Contents:PrefacePart I: Convex analysisConvex sets
and their propertiesThe convex hull of a set. The interior of convex setsThe affine hull of
sets. The relative interior of convex setsSeparation theorems for convex setsConvex
functionsClosedness boundedness continuity and Lipschitz property of convex
functionsConjugate functionsSupport functionsDifferentiability of convex functions and the
subdifferentialConvex conesA little more about convex cones in infinite-dimensional spacesA
problem of linear programmingMore about convex sets and convex hullsPart II: Set-valued
analysisIntroduction to the theory of topological and metric spacesThe Hausdorff metric and the
distance between setsSome fine properties of the Hausdorff metricSet-valued maps. Upper
semicontinuous and lower semicontinuous set-valued mapsA base of topology of the
spaceHc(X)Measurable set-valued maps. Measurable selections and measurable choice theoremsThe
superposition set-valued operatorThe Michael theorem and continuous selections. Lipschitz
selections. Single-valued approximationsSpecial selections of set-valued mapsDifferential
inclusionsFixed points and coincidences of maps in metric spacesStability of coincidence points
and properties of covering mapsTopological degree and fixed points of set-valued maps in Banach
spacesExistence results for differential inclusions via the fixed point
methodNotationBibliographyIndex
