Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis

No books dealing with a comprehensive illustration of the fast developing field of nonlinear analysis had been published for the mathematicians interested in this field for more than a half century until D. H. Hyers, G. Isac and Th. M. Rassias published their book, 'Stability of Functional Equations in SeveralVariables'. This book will complement the books of Hyers, Isac and Rassias and of Czerwik (Functional Equations and Inequalities in Several Variables) by presenting mainly the results applying to the Hyers-Ulam-Rassias stability. Many mathematicians have extensively investigated the subjects on the Hyers-Ulam-Rassias stability. This book covers and offers almost all classical results onthe Hyers-Ulam-Rassias stability in an integrated and self-contained fashion. Organized such that highly advanced undergraduate as well as graduate level students will be able to follow the materials. Contains unified notation andrefined formulae. All the necessary materials and information are included inthis book. Offers almost all classical results on the Hyers—Ulam—Rassias stability in an integrated and self-contained fashion. INDICE: -1. Introduction. -2. Additive Cauchy Equation (Behavior of additive functions, Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Stability ona restricted domain, Method of invariant means, Fixed point method, Compositefunctional congruences, Pexider equation, Remarks). -3. Generalized Additive Cauchy Equations (Functional equation f(ax+by)=af(x)+bf(y), Additive Cauchy equations of general form, Functional equation f(x+y)2=(f(x)+f(y))2). -4. Hossz?’s Functional Equation (Stability in the sense of Borelli, Hyers-Ulam stability, Generalized Hossz?’s equation is not stable on the unit interval, Hossz?’s functional equation of Pexider type). -5. Homogeneous Functional Equation(Homogeneous equation between Banach algebras, Superstability on a restricted domain, Homogeneous equation between vector spaces, Homogeneous equation of Pexide type). -6. Linear Functional Equations (A system for linear functions, Functional equation f(x+cy)=f(x)+cf(y), Stability for other equations).-7. Jensen’s Functional Equation (Hyers-Ulam-Rassias stability, Stability on a restriced domain, Fixed point method, Loba?evskíí;s functional equation). -8. Quadratic Functional Equations (Hyers-Ulam-Rassias stability, Stability on a restricted domain, Fixedpoint method, Quadratic functional equation of other type, Quadraticfunctional equation of Pexider type). -9. Exponential Functional Equations (Superstability, Stability in the sense of Ger, Stability on a restricted domain, Exponential functional equation of other type). -10. Multiplicative Functional Equations (Superstability, ?-multiplicative functional, Theory of AMNM algebras, Functional equation f(xy)= f(x)y, Functional equation f(x+y)= f(x)f(y)f(1/x+1/y)). -11. Logarithmic Functional Equations (Functional equation f(xy)= yf(x), Superstability of equation f(xy)= yf(x), Functional equation of Heuvers). -12. Trigonometric Functional Equations (Cosine functional equation, Sine functional equation, Trigonometric equations with two unknowns, Butler-Rassias functional equation, Remarks). -13. Isometric Functional Equation (Hyers-Ulam stability, Stability on a restricted domain, Fixed point method, Wigner equation). -14. Miscellaneous (Associativity equation, Equation of multiplicative derivation, Gamma functional equation). -Bibliography. -Index.

• ISBN: 978-1-4419-9636-7
• Editorial: Springer New York
• Encuadernacion: Cartoné
• Páginas: 364
• Fecha Publicación: 11/04/2011
• Nº Volúmenes: 1
• Idioma: Inglés