Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis
Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis
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Author(s): Jung, Soon-Mo
ISBN No.: 9781461428626
Pages: xiv, 362
Year: 201305
Format: Trade Paper
Price: $ 75.89
Dispatch delay: Dispatched between 7 to 15 days
Status: Available

-1. Introduction. -2. 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). -3. Generalized Additive Cauchy Equations (Functional equation f(ax+by)=af(x)+bf(y), Additive Cauchy equations of general form, Functional equation f(x+y)2=(f(x)+f(y))2). -4. Hossz's Functional Equation (Stability in the sense of Borelli, Hyers-Ulam stability, Generalized Hossz's equation is not stable on the unit interval, Hossz's functional equation of Pexider type).


-5. Homogeneous Functional Equation(Homogeneous equation between Banach algebras, Superstability on a restricted domain, Homogeneous equation between vector spaces, Homogeneous equation of Pexide type). -6. Linear Functional Equations (A system for linear functions, Functional equation f(x+cy)=f(x)+cf(y), Stability for other equations).-7. Jensen's Functional Equation (Hyers-Ulam-Rassias stability, Stability on a restriced domain, Fixed point method, Lobacevskíí;s functional equation). -8. Quadratic Functional Equations (Hyers-Ulam-Rassias stability, Stability on a restricted domain, Fixedpoint method, Quadratic functional equation of other type, Quadratic functional equation of Pexider type).


-9. Exponential Functional Equations (Superstability, Stability in the sense of Ger, Stability on a restricted domain, Exponential functional equation of other type). -10. Multiplicative Functional Equations (Superstability, δ-multiplicative functional, Theory of AMNM algebras, Functional equation f(xy)= f(x)y, Functional equation f(x+y)= f(x)f(y)f(1/x+1/y)). -11. Logarithmic Functional Equations (Functional equation f(xy)= yf(x), Superstability of equation f(xy)= yf(x), Functional equation of Heuvers). -12. Trigonometric Functional Equations (Cosine functional equation, Sine functional equation, Trigonometric equations with two unknowns, Butler-Rassias functional equation, Remarks).


-13. Isometric Functional Equation (Hyers-Ulam stability, Stability on a restricted domain, Fixed point method, Wigner equation). -14. Miscellaneous (Associativity equation, Equation of multiplicative derivation, Gamma functional equation). -Bibliography. -Index.


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