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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.

Mathematics. --- Difference and Functional Equations. --- Operator Theory. --- Ordinary Differential Equations. --- Functional equations. --- Operator theory. --- Differential Equations. --- Mathématiques --- Equations fonctionnelles --- Théorie des opérateurs --- Banach algebras. --- Functional equations -- Numerical solutions. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Functional equations --- Numerical solutions. --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Difference equations. --- Differential equations. --- Numerical analysis --- Banach spaces --- Topological algebras --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Equations, Functional --- Calculus of differences --- Differences, Calculus of --- Equations, Difference