[PDF] Top 20 Fixed Points and Stability of the Cauchy Functional Equation in -Algebras
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Fixed Points and Stability of the Cauchy Functional Equation in -Algebras
... The stability problem of functional equations originated from a question of Ulam 1 concerning the stability of group ...Hyers-Ulam stability of functional ...unbounded Cauchy ... See full document
14
Fixed Points and Hyers-Ulam-Rassias Stability of Cauchy-Jensen Functional Equations in Banach Algebras
... Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f (x + ... See full document
15
Fixed points and stability of functional equations in fuzzy ternary Banach algebras
... Let X and Y be linear spaces. For each m with ≤ m ≤ n, a mapping f : X → Y satisfies equation (.) for all n ≥ if and only if f (x) – f () = A(x) is Cauchy additive, where f () = if m < n. In ... See full document
10
A Fixed Point Approach to the Stability of a Quadratic Functional Equation in Algebras
... the stability of group homomorphisms was proposed by Ulam 1: Under what conditions does there exist a group homomorphism near an approximately group homomorphism? In 1941, Hyers 2 considered the case of ... See full document
10
Fixed Points and Stability of a Generalized Quadratic Functional Equation
... the fixed point method see 24, 25, 38, 53–55, we prove the generalized Hyers- Ulam stability of A-quadratic mappings in Banach A-modules associated with the functional equation ...of ... See full document
19
Fixed point approach to the Hyers-Ulam-Rassias approximation of homomorphisms and derivations on Non-Archimedean random Lie $C^*$-algebras
... the fixed point method, we prove the general- ized Hyers-Ulam stability of homomorphisms and derivations in non- Archimedean random C ∗ -algebras and non-Archimedean random Lie C ∗ -algebras ... See full document
12
Approximation of the generalized Cauchy–Jensen functional equation in \(C^{*}\) algebras
... for all μ ∈ S := { λ ∈ C | | λ | = 1} and for any fixed positive integer α ≥ 2, which was introduced by Gao et al. [J. Math. Inequal. 3:63–77, 2009], on C ∗ -algebras by using fixed poind alternative theorem. ... See full document
19
Stability of the Cauchy-Jensen Functional Equation in -Algebras: A Fixed Point Approach
... Hyers-Ulam-Rassias stability of C ∗ -algebra homomorphisms and of generalized derivations on C ∗ -algebras for the following Cauchy-Jensen functional equation 2fx y/2 z fx fy 2fz, which ... See full document
11
Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach
... of functional equations is the following: “When is it true that a function, which approximately satisfies a functional equation E must be close to an exact solution of E ?” If the problem accepts a ... See full document
13
Fixed Points and Random Stability of a Generalized Apollonius Type Quadratic Functional Equation
... of stability theory of functional equations for the proof of new fixed-point theorems with ...using fixed point methods, the stability problems of several functional equations ... See full document
11
Quadratic Quartic Functional Equations in RN Spaces
... for all x ∈ E. Moreover, if ftx is continuous in t ∈ R for each fixed x ∈ E, then T is R-linear. In 1978, Rassias 3 provided a generalization of Hyers’ theorem which allows the Cauchy difference to be ... See full document
14
Approximate * derivations and approximate quadratic * derivations on C* algebras
... introduce functional equations of *-derivations and of quadratic ...the stability of *-derivations associated with the Cauchy func- tional equation and the Jensen functional ... See full document
13
Fixed Points, Inner Product Spaces, and Functional Equations
... quadratic functional equation. A generalized Hyers-Ulam stability problem for the quadratic functional equation was proved by Skof 6 for mappings f : X → Y , where X is a normed space ... See full document
14
On the stability of set-valued functional equations with the fixed point alternative
... of stability theory of functional equations for the proof of new fixed point theorems with ...using fixed point methods, the stability problems of several functional equations ... See full document
17
On the Stability of Affine Functional Equations in Various Spaces
... In 1940, Stanislaw M. Ulam [10], triggered the study of stability problems for various functional equations. He presented a number of important unsolved problems. One of the interesting problem in the ... See full document
7
Erratum to: A Note to Paper "On the Stability of Cubic Mappings and Quartic Mappings in Random Normed Spaces"
... cubic functional equation is said to be a cubic mapping. The stability problem for the cubic functional equation was solved by Jun and Kim 2 and Lee 3 for mappings f : X → Y , where X ... See full document
6
Fuzzy Stability of Additive Functional Inequalities with the Fixed Point Alternative
... mapping equation. In particular, every solution of the quadratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional ... See full document
17
Random Stability of an Additive Quadratic Quartic Functional Equation
... the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation f x 2y f x − 2y 2f x y 2f − x − y 2fx − y 2f y − x − 4f−x ... See full document
18
On the Stability of a General Mixed Additive Cubic Functional Equation in Random Normed Spaces
... the equation is stable see 1. The first stability problem concerning group homomorphisms was raised by Ulam 2 in 1940 and affirmatively solved by Hyers ...the Cauchy difference operator CDf x, y fx y − ... See full document
16
Non-Archimedean stability of Cauchy-Jensen Type functional equation
... functional equation. In particular, every solution of the qua- dratic functional equation is said to be a quadratic ...Hyers-Ulam stability problem for the quadratic functional ... See full document
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