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Stability of Functional Equations in Banach Algebras

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The main purpose of this book is to present some of the old and recent results
on homomorphisms and derivations in Banach algebras, quasi-Banach algebras,
C-algebras, C-ternary algebras, non-Archimedean Banach algebras, and multinormed algebras.
In 1940, S. M. Ulam [321] proposed a stability problem on group homomorphisms in metric groups. In 1941, D. H. Hyers [133] proved the stability of additive
mappings in Banach spaces associated with the Cauchy equation. In 1978, Th. M.
Rassias [267] proved the stability of R-linear mappings associated with the Cauchy
equation, and in 2002 C. Park [220] proved the stability of C-linear mappings
in the spirit of Hyers, Ulam, and Rassias in Banach modules. Homomorphisms
and derivations in Banach algebras, quasi-Banach algebras, C-algebras, C-
ternary algebras, non-Archimedean Banach algebras and multi-normed algebras
are additive and R-linear or C-linear, and so we study the stability problems for
additive functional equations and additive mappings. Using the direct method and
the fixed point method, the authors have studied the stability and the superstability
of homomorphisms and derivations in Banach algebras, quasi-Banach algebras,
C-algebras, C-ternary algebras, non-Archimedean Banach algebras, and multinormed algebras, which are also associated with additive functional equations and
additive functional inequalities.

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Series Title

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Call Number

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Publisher

London : Springer., 2015

Collation

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Language

English

ISBN/ISSN

978-3-319-18708-2

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

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Subject(s)

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Specific Detail Info

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Statement of Responsibility

Yeol Je Cho , Choonkil Park , Themistocles M. Rassias , Reza Saadati

Other Information

Cataloger

Jemadi

Source

https://link.springer.com/content/pdf/10.1007/978-3-319-18708-2.pdf?pdf=button

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