| Description |
1 online resource |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Note |
Online resource; title from PDF title page (EBSCO, viewed March 16, 2016). |
| Bibliography |
Includes bibliographical references and index. |
| Summary |
Presently no other book deals with the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups. Moreover, in most stability theorems for functional equations, the completeness of the target space of the unknown functions contained in the equation is assumed. Recently, the question, whether the stability of a functional equation implies this completeness, has been investigated by several authors. In this book the authors investigate these developments in the theory of approximate functional equations. |
| Contents |
Front Cover; Theory of Approximate Functional Equations: in Banach algebras, inner product spaces and amenable groups; Copyright; Contents; Chapter 1: Introduction; Chapter 2: Approximate Cauchy functional equations and completeness; 2.1 Theorem of Hyers; 2.2 Theorem of Themistocles M. Rassias; 2.3 Completeness of normed spaces; Chapter 3: Stability of mixed type functional equations; 3.1 Binary mixtures of functional equations; 3.2 Ternary mixtures of functional equations; 3.3 Mixed foursome of functional equations; Chapter 4: Stability of functional equations in Banach algebras. |
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4.1 Approximate homomorphisms and derivations in ordinary Banach algebras4.2 Approximate homomorphisms and derivations in C∗-algebras; 4.3 Stability problem on C∗-ternary algebras; 4.3.1 Approximately J∗-homomorphisms; 4.3.2 The stability of J∗-derivations; 4.4 General solutions of some functional equations; 4.4.1 A sufficient condition for Pompeiu's functional equation; 4.4.2 Functional equation f(x+y+xy+yx)=f(x)+f(y)+f(x)f(y)+f(y)f(x); 4.4.3 Functional equation f(x+y+xy)=f(x)+f(y)+f(x)y+xf(y); 4.5 Some open problems; Chapter 5: Stability of functional equations in inner product spaces. |
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5.1 Introduction5.2 Orthogonal derivations in orthogonality Banach algebras; 5.3 Some open problems; Chapter 6: Amenability of groups (semigroups) and the stability of functional equations; 6.1 Introduction; 6.2 The stability of homomorphisms and amenability; 6.3 Some open problems; Bibliography; Index; Back Cover. |
| Subject |
Functional differential equations.
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Banach algebras.
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Inner product spaces.
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Équations différentielles fonctionnelles.
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Espaces à produit scalaire.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Banach algebras
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Functional differential equations
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Inner product spaces
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| Added Author |
Abbaszadeh, Sadegh, author.
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| ISBN |
9780128039717 (electronic bk.) |
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012803971X (electronic bk.) |
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9780128039205 |
| Standard No. |
UKMGB 017750305 |
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AU@ 000068473384 |
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