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The book aims to present several new results concerning solution
and various stabilities of some functional equations in various
spaces. The chapters consider various spaces to investigate
stabilities justifying that stability results hold well in those
spaces. It also includes results proving new insight to analyze
approximate solutions to a given equation whenever uncertainty
occurs. The presentation of the book should be useful for graduated
students and researchers interested in the theory of functional
equations to understand the useful ideas involved and
problems to study further.
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.
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