Introduction
1 Background in Multi-valued Analysis
1.1 Some notions and definitions
1.2 Examples of multivalued mappings
1.3 Vietoris topology
1.4 Continuity concepts
1.5 Upper semicontinuity and closed graphs
1.6 Upper and lower semicontinuous (u.s.c. and l.s.c.) functions and their relations
1.7 Lower semicontinuity and open graphs
1.8 Linear operations on nmltifunctions
1.9 Closed and proper multivalued maps
1.10 Open multivalued maps
1.11 Weakly upper and lower semicontinuous functions
1.12 The topology a(X, X*)
2 Hausdorff-Pompeiu Metric Topology
2.1 Hausdorff continuity
2.2 Hd-U.S.C, l.s.c., and single-valued u.s.c. and l.s.c.functions
2.3 Fixed point theorems for multi-valued contractive mappings
3 Measurable Multifunctions
3.1 Measurable selection
3.2 Scalar measurable
3.2.1 Scalarly measurable selection
3.3 Lusin's theorem type
3.4 Hausdorff-measurable multivalued maps
3.5 The Scorza-Dragoni property
3.6 Lp selection
4 Continuous Selection Theorems
4.1 Partitions of unity
4.2 Michael's selection ttmorem
5 Linear Multivalued Operators
5.1 Uniform boundedness principle
5.2 Norm of linear multivalued operators
6 Fixed Point Theorems
6.1 Approximation methods and fixed point theorems
6.2 Schauder-Tychonoff fixed point theorem
6.3 Fan's fixed point theorem
6.4 Krasnosel'skii-type fixed point theorems
6.4.1 Krasnosel'skii-type fixed point theorem for weakly-weakly u
6.4.2 Krasnosel'skii-type fixed point theorem for u
6.4.3 Expansive Krasnosel'skii type fixed point theorem
6.4.4 Expansive Krasnosel'skii-type fixed point theorem for weakly continuous maps
6.4.5 Expansive Krasnosel'skii-type fixed point theorem for weakly-weakly U
6.4.6 Krasnosel'skii type in a Fr6chet space
6.4.7 Measure of noncompactness and Krasnosel'skii's theorem
6.5 Fixed point theorems for sums of two multivalued operators
6.6 Kakutani fixed point theorem type in topological vector spaces
6.7 Krasnosel'skii-type fixed point theorem in topological vector spaces
7 Generalized Metric and Banach Spaces
7.1 Generalized metric space
7.2 Generalized Banach space
7.3 Matrix convergence
8 Fixed Point Theorems in Vector Metric and Banach Spaces
8.1 Banach principle theorem
8.2 Continuation methods for contractive maps
8.3 Perov fixed point type for expansive mapping
8.4 Leray-Schauder type theorem
8.5 Measure of noncompactness
8.6 Approximation method and Perov type fixed point theorem
8.7 Covitz and Nadler type fixed point theorems
8.8 Fixed point index
8.9 Legggett-Williams type fixed point results
8.10 Legggett-Williams type fixed point theorems in vector Banach spaces
8.11 Multiple fixed points
9 Random Fixed Point Theorems
9.1 Principle expansive mapping
9.2 Approximation method and Krasnosel'skii-type fixed point theorems
9.3 Random fixed point for a Cartesian product of operators
9.4 Measurable selection in vector metric space
9.5 Perov random fixed point theorem
9.6 Schauder and Krasnosel'skii type random fixed point
10 Semigroups
10.1 C0-semigroups
10.1.1 Analytic semigroups
10.2 Fractional powers of closed operators
11 Systems of Impulsive Differential Equations on Half-lines
11.1 Uniqueness and continuous dependence on initial data
11.2 Existence and compactness of solution sets
12 Differential Inclusions
12.1 Filippov's theorem on a bounded intervals
12.2 Impulsive semilinear differential inclusions
12.2.1 Existence results
12.3 Impulsive Stokes differential inclusions
12.4 Differential inclusions in Almgren sense
12.4.1 Multiple-valued function in Almgren sense
12.4.2 Existence result on unbounded domains
12.5 Inclusions in Almgren sense with Riemann-Liouville derivatives
12.5.1 Fractional calculus
12.5.2
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