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Stability of Functional Equations in Banach Algebras

  • Book
  • © 2015

Overview

Authors:
  1. Yeol Je Cho

    1. Department of Mathematics Education and the RINS, Gyeongsang National University College of Education, Jinju, Korea, Republic of (South Korea)

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  2. Choonkil Park

    1. Department of Mathematics, Hanyang University, Seoul, Korea, Republic of (South Korea)

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  3. Themistocles M. Rassias

    1. Department of Mathematics, National Technical University of Athens, Athens, Greece

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  4. Reza Saadati

    1. Department of Mathematics, Iran University of Science and Tech, Tehran, Iran

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  • Presents recent results on homomorphisms and derivations in Banach algebras, quasi-Banach algebras, C*-algebras, C*-Ternary algebras, non-Archimedean Banach algebras, and multi-normed algebras

  • Provides a survey of the latest results on various topics of stability theory

  • Accessible to students with a basic background in operator theory and functional equations and inequalities

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 1-17

  3. Stability of Functional Equations in Banach Algebras

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 19-50

  4. Stability of Functional Equations in C ∗-Algebras

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 51-163

  5. Stability of Functional Inequalities in Banach Algebras

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 165-199

  6. Stability of Functional Equations in C ∗-Ternary Algebras

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 201-228

  7. Stability of Functional Equations in Multi-Banach Algebras

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 229-301

  8. Stability of Functional Equations in Non-Archimedean Banach Algebras

    • Yeol Je Cho, Choonkil Park, Themistocles M. Rassias, Reza Saadati
    Pages 303-326

  9. Back Matter

    Pages 327-343
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Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

  • Department of Mathematics Education and the RINS, Gyeongsang National University College of Education, Jinju, Korea, Republic of (South Korea)

    Yeol Je Cho

  • Department of Mathematics, Hanyang University, Seoul, Korea, Republic of (South Korea)

    Choonkil Park

  • Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  • Department of Mathematics, Iran University of Science and Tech, Tehran, Iran

    Reza Saadati

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