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Theory of Approximate Functional Equations

In Banach Algebras, Inner Product Spaces and Amenable Groups

  • 1st Edition - February 23, 2016
  • Latest edition
  • Authors: Madjid Eshaghi Gordji, Sadegh Abbaszadeh
  • Language: English

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 th… Read more

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Description

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.

Key features

  • A useful text for graduate seminars and of interest to a wide audience including mathematicians and applied researchers
  • Presents recent developments in the theory of approximate functional equations
  • Discusses the stability problem of functional equations in Banach algebras, inner product spaces and amenable groups

Readership

Graduate students, mathematicians and applied researchers

Table of contents

  • 1: Introduction
    • Abstract
  • 2: Approximate Cauchy functional equations and completeness
    • Abstract
    • 2.1 Theorem of Hyers
    • 2.2 Theorem of Themistocles M. Rassias
    • 2.3 Completeness of normed spaces
  • 3: Stability of mixed type functional equations
    • Abstract
    • 3.1 Binary mixtures of functional equations
    • 3.2 Ternary mixtures of functional equations
    • 3.3 Mixed foursome of functional equations
  • 4: Stability of functional equations in Banach algebras
    • Abstract
    • 4.1 Approximate homomorphisms and derivations in ordinary Banach algebras
    • 4.2 Approximate homomorphisms and derivations in C*-algebras
    • 4.3 Stability problem on C*-ternary algebras
    • 4.4 General solutions of some functional equations
    • 4.5 Some open problems
  • 5: Stability of functional equations in inner product spaces
    • Abstract
    • 5.1 Introduction
    • 5.2 Orthogonal derivations in orthogonality Banach algebras
    • 5.3 Some open problems
  • 6: Amenability of groups (semigroups) and the stability of functional equations
    • Abstract
    • 6.1 Introduction
    • 6.2 The stability of homomorphisms and amenability
    • 6.3 Some open problems
  • Bibliography
  • Index

Product details

  • Edition: 1
  • Latest edition
  • Published: March 3, 2016
  • Language: English

About the authors

MG

Madjid Eshaghi Gordji

Full Professor of Mathematics,

Editor in chief of “International Journal of Nonlinear Analysis and Applications”

Editor in chief of “Asian Journal of Scientific Research”

Affiliations and expertise
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Iran

SA

Sadegh Abbaszadeh

Ph.D in Mathematics
Affiliations and expertise
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Iran

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