Functional equations and inequalities in several variables / Stefan Czerwik.

Format:

Book

Author/Creator:

Czerwik, Stefan.

Language:

English

Subjects (All):

Functional equations.

Inequalities (Mathematics).

Physical Description:

1 online resource (ix, 410 p.)

Edition:

1st ed.

Place of Publication:

River Edge, N.J. : World Scientific, c2002.

Language Note:

English

Summary:

An outline of the theory of functional equations and inequalities in several variables. The work is divided into three parts, addressing: functional equations and inequalities in linear spaces; Ulam-Hyers-Rassias stability of functional equations; and functional equations in set-valued functions. An outline of 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, along with many results concerning those problems.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

9789812778116

981277811X

OCLC:

847210978