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generalized Hyers--Ulam

Generalized Hyers-Ulam Stability of a System of Bi-Reciprocal Functional Equations

Generalized Hyers-Ulam Stability of a System of Bi-Reciprocal Functional Equations

... It is easy to see that r(x , y ) = x y 1 is a solution of the system of functional equations (5). In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for the system of ...

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10. Generalized  Hyers-Ulam stability of a 2-variable reciprocal functional equation

10. Generalized Hyers-Ulam stability of a 2-variable reciprocal functional equation

... In 1940, S.M. Ulam [8], while he was giving a talk before the Mathematics Club of Wisconsin, he listed a number of important unsolved problems. One of the problem is the stability of functional equation. Over the ...

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Generalized Hyers-Ulam stability of second order linear ordinary differential equation with initial condition

Generalized Hyers-Ulam stability of second order linear ordinary differential equation with initial condition

... for Hyers-Ulam stability in other areas like, nonlinear analysis problems including partial differential equation and integral ...the Hyers-Ulam stability of more of first, second-order and ...

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On the generalized Hyers Ulam Rassias stability problem of radical functional equations

On the generalized Hyers Ulam Rassias stability problem of radical functional equations

... 3. Hyers, DH: On the stability of the linear functional equation. Proc. Natl. Acad. Sci. USA 27, 222-224 (1941) 4. Aoki, T: On the stability of the linear transformation in Banach spaces. J. Math. Soc. Jpn. 2, ...

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A new method for the generalized Hyers-Ulam-Rassias stability

A new method for the generalized Hyers-Ulam-Rassias stability

... give Hyers-Ulam stability results for a nonlinear functional ...for Hyers-Ulam- Rassias stability, ...in generalized metric spaces to study the Hyers-Ulam stability for ...

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A generalized Hyers Ulam stability of a Pexiderized logarithmic functional equation in restricted domains

A generalized Hyers Ulam stability of a Pexiderized logarithmic functional equation in restricted domains

... The Hyers-Ulam stability problems of functional equations go back to 1940 when Ulam proposed a question concerning the approximate homomorphisms from a group to a metric group (see ...by Hyers ...

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Nearly n homomorphisms and n derivations in fuzzy ternary Banach algebras

Nearly n homomorphisms and n derivations in fuzzy ternary Banach algebras

... In this section, by using the idea of Park et al. [], we prove the generalized Hyers-Ulam- Rassias stability of -homomorphisms and -derivations related to the functional equation (.) on fuzzy ...

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Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay

Hyers-Ulam and Hyers-Ulam-Rassias stability of nonlinear integral equations with delay

... the Hyers theorem (Hyers-Ulam-Rassias stability ...terminologies Hyers-Ulam stability and Hyers-Ulam-Rassias stability can also be applied to the case of other functional ...

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Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation

Fuzzy Stability of Generalized Mixed Type Cubic, Quadratic, and Additive Functional Equation

... f (2x + y) + f (2x − y) = 2f (x + y) + 2f (x − y) + 12f (x) (1:3) and they established the general solution and the generalized Hyers-Ulam stability for the functional equation (1.3). They proved ...

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Fuzzy Stability of Generalized Square Root Functional Equation in Several Variables: A Fixed Point Approach

Fuzzy Stability of Generalized Square Root Functional Equation in Several Variables: A Fixed Point Approach

... ρ i 6= 1 and s : X → R with X as space of non-negative real numbers and investigated generalized Hyers-Ulam stability of equation (2). It is easy to verify that the function f : X → R such that f (x) ...

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Generalized Ulam-Hyers Stability of the Harmonic Mean Functional Equation in Two Variables

Generalized Ulam-Hyers Stability of the Harmonic Mean Functional Equation in Two Variables

... the generalized Hyers- Ulam ...D.H. Hyers and proved the following theorem using weaker conditions controlled by a product of powers of ...

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Hyers Ulam Rassias stability of generalized module left (m,n) derivations

Hyers Ulam Rassias stability of generalized module left (m,n) derivations

... approximate generalized derivations on unital Banach algebras into Banach bimodules, and in [] Jung examined the stability of module left ...the generalized Hyers-Ulam-Rassias stability of a ...

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Isomorphisms in unital $C^*$-algebras

Isomorphisms in unital $C^*$-algebras

... for all x ∈ X. The above inequality has provided a a lot of influence in the de- velopment of what is called Hyers-Ulam-Rassias stability or generalized Hyers-Ulam stability of ...

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Approximate homomorphisms and derivations on random Banach algebras

Approximate homomorphisms and derivations on random Banach algebras

... During the last three decades, a number of papers and research monographs have been published on various generalizations and applications of the generalized Hyers-Ulam sta- bility to a number of ...

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Fixed Points, Inner Product Spaces, and Functional Equations

Fixed Points, Inner Product Spaces, and Functional Equations

... of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for Banach ...spaces. Hyers’ theorem was generalized by ...

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Generalized Ulam-Hyers Stability of two types of n-dimensional Quadratic functional equation in Banach Space: Direct and Fixed Point Methods

Generalized Ulam-Hyers Stability of two types of n-dimensional Quadratic functional equation in Banach Space: Direct and Fixed Point Methods

... 12. Czerwik, S., Functional Equations and Inequalities in Several Variables. World Scientific, River Edge, NJ, 2002. 13. Gavruta, P., A generalization of the Hyers-Ulam-Rassias stability of approximately ...

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Stability of Trigonometric Functional Equations in Generalized Functions

Stability of Trigonometric Functional Equations in Generalized Functions

... We consider the Hyers-Ulam stability of a class of trigonometric functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and G[r] ...

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Approximation of linear mappings in Banach modules over C∗ algebras

Approximation of linear mappings in Banach modules over C∗ algebras

... of Ulam [] concerning the stability of group homomorphisms. Hyers [] gave a first affirmative partial answer to the question of Ulam in Banach ...spaces. Hyers’ theorem was generalized ...

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Stability of a Cauchy Jensen Functional Equation in Quasi Banach Spaces

Stability of a Cauchy Jensen Functional Equation in Quasi Banach Spaces

... the Hyers-Ulam stability by considering variables for Cauchy ...been generalized to the function case by G˘avruta 7 and Jung 8 for Cauchy equation, and by Lee and Jun 9 for Jensen ...

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On the Stability of Generalized Additive Functional Inequalities in Banach Spaces

On the Stability of Generalized Additive Functional Inequalities in Banach Spaces

... following generalized additive functional inequality afx bfy cfz ≤ fαx βy γz, associated with linear mappings in Banach ...the Hyers-Ulam-Rassias stability of the above generalized additive ...

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