This book outlines the modern theory of functional equations and inequalities in several variables. It consists of three parts. The first is devoted to additive and convex functions defined on linear spaces with semilinear topologies. In the second part, the problems of stability of functional equations in the sense of Ulam-Hyers-Rassias and in some function spaces are considered. In the last part, the functional equations in set-valued functions are dealt with - for the first time in the mathematical literature. The book contains many fresh results concerning those problems.
Functional Equations and Inequalities in Linear Spaces: Linear Spaces and Semilinear Topology; Convex Functions; Cauchy's Exponential Equation; Polynomial Functions and Their Extensions; Quadratic Mappings; Quadratic Equation on an Interval; Ulam-Hyers-Rassias Stability of Functional Equations: Additive Cauchy Equation; Multiplicative Cauchy Equation; Jensen's Functional Equation; Gamma Functional Equation; Stability of Homogeneous Mappings; Stability of Functional Equations in Function Spaces; Stability in the Lipschitz Norms; Round-off Stability of Iterations; Functional Equations in Set-Valued Functions: Cauchy's Set-Valued Functional Equation; Pexider's Functional Equation; Subadditive Set-Valued Functions; Hahn-Banach Type Theorem and Applications; Subquadratic Set-Valued Functions; Iteration Semigroups of Set-Valued Functions.