Quadratic Functional Equation
On the Stability of Quadratic Functional Equation
... In this paper the stability of quadratic functional equation, f(xy)+f(xy -1 )=2f(x)+2f(y) on class of groups is obtained and also prove that quadratic functional [r] ...
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A Fixed Point Approach to the Stability of a Quadratic Functional Equation in Algebras
... of functional equations and mappings see ...A quadratic functional equation is a functional equation of the following ...
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ORTHOGONAL STABILITY OF THE NEW GENERALIZED QUADRATIC FUNCTIONAL EQUATION
... each equation is called a quadratic functional ...the quadratic equation ...is quadratic if and only if there exists a unique symmetric biadditive function B such that f ( x ) = ...
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Fixed Points and Stability of a Generalized Quadratic Functional Equation
... a quadratic functional equation. Quadratic functional equations were used to characterize inner product spaces ...the quadratic equation ...is quadratic if and only ...
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Stability of a Quadratic Functional Equation in the Spaces of Generalized Functions
... following quadratic functional equation: f xy z fx fy fz fx y fy z fz x in the spaces of generalized ...heat equation, we obtain the general solution and prove the Hyers-Ulam stability of this ...
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stability of the quadratic functional equation
... is given where σ is an involution of the normed space E and k is a fixed positive integer. Furthermore we investigate the Hyers-Ulam-Rassias stability of the func- tional equation. The Hyers-Ulam stability on ...
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Hyers Ulam Rassias Stability of Orthogonal Quadratic Functional Equation
... D f x y f x y f x y f x (1.1) is called as quadratic functional equation. In 2008, W. Towanlong and P. Nakmahachalasiant [25] established the general solution and proved the ...
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New Type of Quadratic Functional Equation and Its Stability
... the quadratic functional ...the quadratic functional equation is said to be quadratic ...of functional equations for the proof of new fixed point theorems with ...several ...
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Orthogonal Stability of an Additive-Quadratic Functional Equation
... Cauchy functional equation f(x + y) = f(x) + f(y), namely, they showed that if f is a mapping from an orthogonality space X into a real Banach space Y and ||f(x + y) - f(x) - f(y)|| ≤ ε for all x, y Î X ...
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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 ...of functional It was further ...
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A Fixed Point Approach to the Stability of Pexider Quadratic Functional Equation with Involution
... of functional equations is as ...a functional equation must be close to an exact solution of the equation?” The first stability problem concerning group homomorphisms was raised by Ulam 1 in ...
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Intuitionistic Fuzzy Stability of a Quadratic Functional Equation
... In 2003, Cadariu and Radu used the fixed-point method to the investigation of the Jensen functional equation see 12, 13 for the first time. By using fixed point methods, the stability problems of several ...
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Orthogonally additive additive and orthogonally quadratic quadratic functional equation in orthogonality spaces
... in which ⊥ is an abstract orthogonality relation, was first investigated by Gudder and Strawther [8]. They defined ⊥ by a system consisting of five axioms and described the general semi-continuous real-valued solution of ...
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On the Ulam Hyers stability of a quadratic functional equation
... of functional inequalities, as well as let X and Y be real linear spaces in the case of functional equa- ...The quadratic function f(x) = cx 2 (x Î ℝ), where c is a real constant, clearly satis- fies ...
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Functional equations and inequalities in paranormed spaces
... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...the quadratic functional equation was proved by Skof [] for ...
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A Multidimensional Functional Equation Having Quadratic Forms as Solutions
... Jun, “On the generalized Hyers-Ulam-Rassias stability of an n-dimensional quadratic functional equation,” Journal of Mathematical Analysis and Applications, vol.. Park, “On the generaliz[r] ...
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Intuitionistic fuzzy stability of a quadratic and quartic functional equation
... f (x + ky) + f(x − ky) = k 2 f (x + y) + k 2 f(x − y) + 2(1 − k 2 )f(x) (1.3) in quasi–Banach spaces, which k is nonzero integer number with k 6= ±1. Interesting new results concerning mixed functional equations ...
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Random Stability of an Additive Quadratic Quartic Functional Equation
... a quadratic functional ...the quadratic functional equation is said to be a quadratic ...the quadratic functional equation was proved by Skof 6 for mappings ...
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Fuzzy Stability of an Additive Quadratic Quartic Functional Equation
... the quadratic functional ...several functional equations have been extensively investigated by a number of authors and there are many interesting results concerning this problem see 16, ...
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16. A quadratic type functional equation
... the quadratic functional ...is quadratic if and only if there exists a unique symmetric bi-additive function 𝐵 such that 𝑓 (𝑥) = 𝐵(𝑥, 𝑥) for all 𝑥 ∈ 𝒳 ; see ...
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