Some of the most recent and significant results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-ternary algebras, non-Archimedean Banach algebras and multi-normed algebras are presented in this book. A brief introduction for functional equations and their stability is provided with historical remarks. Since the homomorphisms and derivations in Banach algebras are additive and R-linear or C-linear, the stability problems for additive functional equations and additive mappings are studied in detail. The latest results are discussed and examined in stability theory for new functional equations and functional inequalities in Banach algebras and C*-algebras, non-Archimedean Banach algebras, non-Archimedean C*-algebras, multi-Banach algebras and multi-C*-algebras.

Graduate students with an understanding of operator theory, functional analysis, functional equations and analytic inequalities will find this book useful for furthering their understanding and discovering the latest results in mathematical analysis. Moreover, research mathematicians, physicists and engineers will benefit from the variety of old and new results, as well as theories and methods presented in this book.

“The book under review provides an account of some of the most recent and significant results on the stability of homomorphisms and derivations. ... This beautiful book is well written, in a clear self-contained and reader-friendly style. It will prove to be very useful for self-study and seminars. It belongs in every library collection. I recommend it to graduate students and specialists working in functional equations, in functional analysis as well as in physics and engineering.” (Paşc Găvruţă, zbMATH 1323.39025, 2015)