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 Existence result 12.6 Differential inclusions via Caputo fractional derivative 12.6.1 Existence and compactness result 13 Random Systems of Differential Equations 13.1 Random Cauchy problem 13.2 Boundary value problems 13.3 An example 14 Random Fractional Differential Equations 14.1 Hadamard fractional derivative 14.2 Random fractional derivative 14.3 Existence of solution 14.4 M2-solutions 14.4.1 Existence and uniqueness of M2-solutions 15 Existence Theory for Systems of Discrete Equations 15.1 Introduction and motivations 15.1.1 Cagan's model with backward-looking market participants 15.1.2 Electronic model 15.2 Gronwall inequalities 15.3 Cauchy discrete problem 15.4 Existence and uniqueness 15.5 Existence and compactness of solution sets 15.6 Systems of difference equations with infinite delay 15.6.1 Definitions and fundamental results 15.6.2 Boundedness of solutions 15.6.3 Weighted boundedness and asymptotic behavior 15.6.4 Asymptotic periodicity 15.6.5 Volterra difference system with infinite delay 15.7 Boundary value problems 15.8 Second order boundary value problems 15.9 Multiplicity of solutions for nth order boundary value problems 16 Discrete Inclusions 16.1 Cauchy problem for discrete inclusions 16.2 Existence and compactness result 17 Semilinear System of Discrete Equations 17.1 Existence and uniqueness results 17.2 Boundary value problems 18 Discrete Boundary Value Problems 18.1 Initial value problems 18.2 Nonlocal boundary value problems 18.3 Differentiation of solutions with respect to boundary conditions Bibliography Index ��݋��ӛ