Stability of Functional Equations in Several Variables

D H Hyers

ISBN 10: 081764024X / ISBN 13: 9780817640248

Editore: Birkhauser Boston Sep 1998, 1998

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Neuware - 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 de 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 pre 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 equa 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 co author and friend Professor Donald H. Hyers passed away.

Codice articolo 9780817640248

Dati bibliografici

• Titolo: Stability of Functional Equations in Several Variables
• Editore: Birkhauser Boston Sep 1998
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 081764024X
• ISBN 13: 9780817640248
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 242 L x 162 A x 21 P (millimetri) 242 millimetri di larghezza per 162 millimetri di altezza per 21 millimetri di profondità
• Peso: 621 grammi

Descrizione articolo

Riassunto

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 de­ 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 pre­ 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 equa­ 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 co­ author and friend Professor Donald H. Hyers passed away.

Recensione

"...The book under review is an exhaustive presentation of the results in the field, not called Hyers-Ulam stability. It contains chapters on approximately additive and linear mappings, stability of the quadratic functional equation, approximately multiplicative mappings, functions with bounded differences, approximately convex functions. The book is of interest not only for people working in functional equations but also for all mathematicians interested in functional analysis."

–Zentralblatt Math

"Contains survey results on the stability of a wide class of functional equations and therefore, in particular, it would be interesting for everyone who works in functional equations theory as well as in the theory of approximation."

–Mathematical Reviews