| |

| |

| |

Introduction | |

| |

| |

| |

Additive Cauchy Equation | |

| |

| |

| |

Behavior of Additive Functions | |

| |

| |

| |

Hyers-Ulam Stability | |

| |

| |

| |

Hyers-Ulam-Rassias Stability | |

| |

| |

| |

Stability on a Restricted Domain | |

| |

| |

| |

Method of Invariant Means | |

| |

| |

| |

Fixed Point Method | |

| |

| |

| |

Composite Functional Congruences | |

| |

| |

| |

Pexider Equation | |

| |

| |

| |

Remarks | |

| |

| |

| |

Generalized Additive Cauchy Equations | |

| |

| |

| |

Functional Equation f(ax + by) = af(x) + bf(y) | |

| |

| |

| |

Additive Cauchy Equations of General Form | |

| |

| |

| |

Functional Equation f(x + y)<sup>2</sup> = (f(x) + f(y))<sup>2</sup> | |

| |

| |

| |

Hosszï¿½'s Functional Equation | |

| |

| |

| |

Stability in the Sense of Borelli | |

| |

| |

| |

Hyers-Ulam Stability | |

| |

| |

| |

Generalized Hosszï¿½'s Functional Equation | |

| |

| |

| |

Hosszï¿½'s Equation is not Stable on the Unit Interval | |

| |

| |

| |

Hosszï¿½'s Functional Equation of Pexider Type | |

| |

| |

| |

Homogeneous Functional Equation | |

| |

| |

| |

Homogeneous Equation Between Banach Algebras | |

| |

| |

| |

Superstability on a Restricted Domain | |

| |

| |

| |

Homogeneous Equation Between Vector Spaces | |

| |

| |

| |

Homogeneous Equation of Pexider Type | |

| |

| |

| |

Linear Functional Equations | |

| |

| |

| |

A System for Linear Functions | |

| |

| |

| |

Functional Equation f(x + cy) = f(x) + cf(y) | |

| |

| |

| |

Stability for Other Equations | |

| |

| |

| |

Jensen's Functional Equation | |

| |

| |

| |

Hyers-Ulam-Rassias Stability | |

| |

| |

| |

Stability on a Restricted Domain | |

| |

| |

| |

Fixed Point Method | |

| |

| |

| |

Lobacevskii's Functional Equation | |

| |

| |

| |

Quadratic Functional Equations | |

| |

| |

| |

Hyers-Ulam-Rassias Stability | |

| |

| |

| |

Stability on a Restricted Domain | |

| |

| |

| |

Fixed Point Method | |

| |

| |

| |

Quadratic Functional Equation of Other Type | |

| |

| |

| |

Quadratic Functional Equation of Pexider Type | |

| |

| |

| |

Exponential Functional Equations | |

| |

| |

| |

Superstability | |

| |

| |

| |

Stability in the Sense of Ger | |

| |

| |

| |

Stability on a Restricted Domain | |

| |

| |

| |

Exponential Functional Equation of Other Type | |

| |

| |

| |

Multiplicative Functional Equations | |

| |

| |

| |

Superstability | |

| |

| |

| |

ï¿½Multiplicative Functionals | |

| |

| |

| |

Theory of AMNM Algebras | |

| |

| |

| |

Functional Equation f(x<sup>y</sup>) = f(x)<sup>y</sup> | |

| |

| |

| |

Functional Equation f(x + y) = f(x)f(y)f(1/x + 1/y) | |

| |

| |

| |

Logarithmic Functional Equations | |

| |

| |

| |

Functional Equation f(x<sup>y</sup>) = yf(x) | |

| |

| |

| |

Superstability of Equation f(x<sup>y</sup>) = yf(x) | |

| |

| |

| |

Functional Equation of Heuvers | |

| |

| |

| |

Trigonometric Functional Equations | |

| |

| |

| |

Cosine Functional Equation | |

| |

| |

| |

Sine Functional Equation | |

| |

| |

| |

Trigonometric Equations with Two Unknowns | |

| |

| |

| |

Butler-Rassias Functional Equation | |

| |

| |

| |

Remarks | |

| |

| |

| |

Isometric Functional Equation | |

| |

| |

| |

Hyers-Ulam Stability | |

| |

| |

| |

Stability on a Restricted Domain | |

| |

| |

| |

Fixed Point Method | |

| |

| |

| |

Wigner Equation | |

| |

| |

| |

Miscellaneous | |

| |

| |

| |

Associativity Equation | |

| |

| |

| |

Equation of Multiplicative Derivation | |

| |

| |

| |

Gamma Functional Equation | |

| |

| |

| |

Fibonacci Functional Equation | |

| |

| |

Bibliography | |

| |

| |

Index | |