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mixed type additive and cubic functional equation

Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation

Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation

... for all x ∈ E. Moreover if f tx is continuous in t for each fixed x ∈ E, then T is linear see also 3. In 1950, Aoki 4 generalized Hyers’ theorem for approximately additive mappings. In 1978, Th. M. Rassias 5 ...

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A fixed point approach to the non-Archimedean random stability of generalized mixed type AQCQ-functional equations

A fixed point approach to the non-Archimedean random stability of generalized mixed type AQCQ-functional equations

... a cubic functional equation, because the cubic function f (x) = cx 3 is a solution of the equation ...the functional equation ...is additive for fixed two ...

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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

... quadratic, cubic and quartic functional equations and its Hyers-Ulam-Rassias stability were discussed by various authors ([3], [7], [12], [21], [24], [27], [29], [32], [34], ...the mixed type ...

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Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces

Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces

... a cubic functional equation. Every solution of the cubic functional equation is said to be a cubic ...is additive for fixed two ...

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Stability of generalized QCA-functional equation in P-Banach spaces

Stability of generalized QCA-functional equation in P-Banach spaces

... a mixed type of quadratic and additive functional ...a mixed type of cubic, quadratic and additive functional equation, with f(0) = ...

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Stability of 2-Variable Additive-Quadratic-Cubic-Quartic Functional Equation Using Fixed Point Method

Stability of 2-Variable Additive-Quadratic-Cubic-Quartic Functional Equation Using Fixed Point Method

... of mixed type functional equations have been extensively investigated by a number of math- ematicians in referenes (see [3–5, 14–22, 28–31, 33–38, 43, 48, ...

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Orthogonal stability of mixed type additive and cubic functional equations

Orthogonal stability of mixed type additive and cubic functional equations

... f(x + y) = f (x) + f (y), (x, y ∈ A, x⊥y) (1.1) in which ⊥ is an abstract orthogonally was first investigated by S. Gudder and D. Strawther [7]. R. Ger and J. Sikkorska discussed the orthogonal stability of the ...

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On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi Banach Spaces

On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi Banach Spaces

... functional equation 1.5, which is called a quartic functional equation see also ...a mixed type of quartic and quadratic functional equation between two real linear ...

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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

... the functional equation ...the functional equation ...generalized mixed cubic, quadratic, and additive functional equation ...

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Stability of a mixed type cubic and quartic functional equation in fuzzy Banach spaces

Stability of a mixed type cubic and quartic functional equation in fuzzy Banach spaces

... for additive mappings. For additive mapping involving dif- ferent powers of norms ...other type fuzzy norms and some properties of fuzzy normed linear spaces ...

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A fixed point approach to the Hyers Ulam stability of an AQ functional equation on β Banach modules

A fixed point approach to the Hyers Ulam stability of an AQ functional equation on β Banach modules

... Therefore, f satisfies (.). Now, we claim that the functional equation (.) is not stable for p =  in Corollary .. Suppose, on the contrary, that there exist an additive mapping A : C → C and a ...

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3 Dimensional Additive Quadratic Functional Equation

3 Dimensional Additive Quadratic Functional Equation

... for functional equations is related to a question of Ulam [51] concerning the stability of group homomorphisms was affirmatively answered for Banach spaces by Hyers ...for additive mappings and by Rassias ...

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A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi  Normed Spaces

A Fixed Point Approach to the Stability of Quintic and Sextic Functional Equations in Quasi Normed Spaces

... Proof. Assume that f satisfies the functional equation 1.4. Replacing x y 0 in 1.4, one gets f 0 0. Replacing x, y with 0, x and x, −x in 1.4, respectively, and adding the two resulting equations, we obtain ...

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Stability of an Additive Cubic Quartic Functional Equation

Stability of an Additive Cubic Quartic Functional Equation

... unique additive mapping A : X → Y, a unique mapping C : X × X × X → Y , and a unique symmetric multi-additive mapping Q : X × X × X × X → Y such that fx Ax Cx, x, x Qx, x, x, x for all x ∈ X, and that C is ...

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A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation

A Fixed Point Approach to the Fuzzy Stability of an Additive-Quadratic-Cubic Functional Equation

... for all x, y ∈ E, controlled by a product of different powers of norms, where θ ≥ 0 and real numbers p, q, r : p q / 1, and retained the condition of continuity of f tx in t ∈ R for each fixed x ∈ E. Besides he ...

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A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation

A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation

... The stability problem of functional equations is originated from a question of Ulam 1 concerning the stability of group homomorphisms. Hyers 2 gave a first affirmative partial answer to the question of Ulam for ...

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On the stability of set-valued functional equations with the fixed point alternative

On the stability of set-valued functional equations with the fixed point alternative

... of functional equations for the proof of new fixed point theorems with ...several functional equations have been extensively investigated by a number of authors (see ...

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Fuzzy stability of a mixed type functional equation

Fuzzy stability of a mixed type functional equation

... Theorem 2.2 . Let q be a positive real number with q = 1 2 , 1. And let f be a fuzzy q- almost quadratic-additive mapping from a fuzzy normed space (X, N) into a fuzzy Banach space (Y, N ’ ). Then there is a ...

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Approximation of Functions by Quadratic Mapping in (β, p) Banach Space

Approximation of Functions by Quadratic Mapping in (β, p) Banach Space

... [19] Rassias, J.M. and Kim, H.M. (2009) Generalized Hyers-Ulam Stability for General Additive Functional Equation in Quasi- β -Normed Space. Journal of Mathematical Analysis and Applications , 356, ...

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Orthogonal Stability of Mixed Additive Quadratic Jensen Type Functional Equation in Multi Banach Spaces

Orthogonal Stability of Mixed Additive Quadratic Jensen Type Functional Equation in Multi Banach Spaces

... in which ⊥ is an orthogonality relation, is first investigated by Gudder and Strawther [13]. In 1985, Rätz [14] in- troduced a new definition of orthogonality by using more restrictive axioms than Gudder and Strawther. ...

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