Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis [Hardcover]

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 Several Variables .

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 on the Hyers-Ulam-Rassias stability in an integrated and self-contained fashion.

In an integrated and self-contained fashion, this book covers almost all classical results on the Hyers-Ulam-Rassias stability. It is arranged so that highly advanced undergraduate as well as graduate level students will be able to follow the materials.

-1. Introduction.?-2. Additive Cauchy Equation (Behavior of additive functions, Hyers-Ulam stability, Hyers-Ulam-Rassias stability, Stability on a restricted domain, Method of invariant means, Fixed point method, Composite functional 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.lC