Functional equations and inequalities in several variables / Stefan Czerwik.

Includes bibliographical references and index.

Print version record.

Pt. I. Functional equations and inequalities in linear spaces. 1. Linear spaces and semilinear topology -- 2. Convex functions -- 3. Lower hull of a convex function -- 4. Theorems of Bernstein-Doetsch, Piccard and Mehdi -- 5. Some set classes of continuous and J-convex functions -- 6. Cauchy's exponential equation -- 7. D'Alembert's equation on abelian groups -- 8. D’Alembert's equation on topological groups -- 9. Polynomial functions and their extensions -- 10. Quadratic mappings -- 11. Quadratic equation on an interval -- 12. Functional equations for quadratic differences -- pt. II. Ulam-Hyers-Rassias stability of functional equations. 13. Additive Cauchy equation -- 14. Multiplicative Cauchy equation -- 15. Jensen’s functional equation -- 16. Pexider's functional equation -- 17. Gamma functional equation -- 18. D'Alembert's and Lobaczevski's functional equations -- 19. Stability of homogeneous mappings -- 20. Quadratic functional equation -- 21. Stability of functional equations in function spaces -- 22. Cauchy difference operator in L[symbol] spaces -- 23. Pexider difference operator in L[symbol] spaces -- 24. Cauchy and Pexider operators in X[symbol] spaces -- 25. Stability in the Lipschitz norms -- 26. Round-off stability of iterations -- 27. Quadratic difference operator in L[symbol] spaces -- pt. III. Functional equations in set-valued functions. 28. Cauchy's set-valued functional equation -- 29. Jensen's functional equation -- 30. Pexider's functional equation -- 31. Quadratic set-valued functions -- 32. Subadditive set-valued functions -- 33. Superadditive set-valued functions and generalization of Banach-Steinhaus theorem -- 34. Hahn-Banach type theorem and applications -- 35. Subquadratic set-valued functions -- 36. K-convex and K-concave set-valued functions -- 37. Iteration semigroups of set-valued functions.

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.

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