Functional equations and inequalities in several variables /

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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 equat...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Czerwik, Stefan
Formato: Electrónico eBook
Idioma:Inglés
Publicado: River Edge, N.J. : World Scientific, ©2002.
Temas:
Functional equations.
Inequalities (Mathematics)
Équations fonctionnelles.
Inégalités (Mathématiques)
MATHEMATICS > Functional Analysis.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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