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AuthorHyers, Donald H. author
TitleStability of Functional Equations in Several Variables [electronic resource] / by Donald H. Hyers, George Isac, Themistocles M. Rassias
ImprintBoston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 1998
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1790-9
Descript VII, 318 p. online resource

SUMMARY

The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and deยญ veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the preยญ sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equaยญ tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved coยญ author and friend Professor Donald H. Hyers passed away


CONTENT

Prologue -- 1. Introduction -- 2. Approximately Additive and Approximately Linear Mappings -- 3. Stability of the Quadratic Functional Equation -- 4. Generalizations. The Method of Invariant Means -- 5. Approximately Multiplicative Mappings. Superstability -- 6. The Stability of Functional Equations for Trigonometric and Similar Functions -- 7. Functions with Bounded nth Differences -- 8. Approximately Convex Functions -- 9. Stability of the Generalized Orthogonality Functional Equation -- 10. Stability and Set-Valued Functions -- 11. Stability of Stationary and Minimum Points -- 12. Functional Congruences -- 13. Quasi-Additive Functions and Related Topics -- References


Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Functional analysis Mathematics Functional Analysis Analysis Dynamical Systems and Ergodic Theory



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