Quartic functional equation
3. Stability of a quartic and ortgogonally quartic functional equation
... a quartic functional equation ...orthogonally quartic func- tional equation (2) for all x, y, z ∈ X with x ⊥ y, y ⊥ z and z ⊥ x in the sense of R¨ atz is ...
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Random Stability of an Additive Quadratic Quartic Functional Equation
... additive-quadratic-quartic functional equation f x 2y f x − 2y 2f x y 2f − x − y 2fx − y 2f y − x − 4f−x − 2fx f2y f−2y − 4fy − 4f−y in complete random normed ...
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Fuzzy Stability of an Additive Quadratic Quartic Functional Equation
... This paper is organized as follows. In Section 2, we prove the generalized Hyers-Ulam stability of the additive-quadratic-quartic functional equation 1.1 in fuzzy Banach spaces for an odd case. In ...
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The Hyers Ulam Rassias stability of the quartic functional equation in fuzzy β normed spaces
... In the next year, Hyers [] gave a positive answer to the above question for additive groups under the assumption that the groups are Banach spaces. In , Rassias [] ex- tended the theorem of Hyers by considering the ...
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Intuitionistic fuzzy stability of a quadratic and quartic functional equation
... and quartic functional equation, since the function f (x) = ax 4 + bx 2 is its ...and quartic functional equation was proved by Eshaghi ...
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Stability of an Additive Cubic Quartic Functional Equation
... In fact, they proved that a mapping f between two real vector spaces X and Y is a solution of 1.2 if and only if there exists a unique symmetric multi-additive mapping B : X ×X ×X ×X → Y such that fx Bx, x, x, x for all ...
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Orthogonal stability of an additive quartic functional equation with the fixed point alternative
... > 0, p Î [0,1)). The result of Rassias has provided a lot of influ- ence in the development of what we now call generalized Hyers-Ulam stability or Hyers- Ulam stability of functional equations. During the last ...
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A Fixed Point Approach to the Stability of an Additive-Quadratic-Cubic-Quartic Functional Equation
... functional equation. In particular, every solution of the quadratic functional equation is said to be a quadratic ...quadratic functional equation was proved by Skof 6 for ...
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Stability of a mixed type cubic and quartic functional equation in fuzzy Banach spaces
... Hyers [8] was the first person to point out the direct method for studying the stability of func- tional equation. In 2003, Radu [19] proposed the fixed point alternative method to solve the Ulam problem. ...
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Generalized Ulam - Hyers Stability of on (AQQ): Additive - Quadratic - Quartic Functional Equation
... Keywords: Additive functional equations, Quadratic functional equations, Quartic functional equations, Mixed type functional equations, Ulam - Hyers stability, Ulam - Hyers - Rassias sta[r] ...
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Stability of 2-Variable Additive-Quadratic-Cubic-Quartic Functional Equation Using Fixed Point Method
... The stability 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, 50–52]). In 2003, V. Radu [39] introduced a ...
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On the Stability of Quartic Functional Equations via Fixed Point and Direct Method
... of quartic functional equation f (3 x y ) f x ( 3 ) y 64 ( ) f x 64 ( ) f y 24 ( f x y ) 6 ( f x y ) in the setting of random normed space and intuitionistic random normed ...the ...
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Generalized Ulam-Hyers Stability of the Harmonic Mean Functional Equation in Two Variables
... [40] K. Ravi, J.M. Rassias and B.V. Senthil Kumar, Ulam stability of Reciprocal Difference and Adjoint Funtional Equations, The Australian J. Math. Anal.Appl. 8(1), Art.13 (2011), 1-18. [41] K. Ravi, J.M. Rassias M. ...
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Cubic-quartic functional equations in fuzzy normed spaces
... cubic functional equation. Every solution of the cubic functional equation is said to be a cubic ...of quartic functional equation was introduced by ...
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Functional equations and inequalities in paranormed spaces
... additive functional equa- tion, the quadratic functional equation ...cubic functional equation (.) and the quartic functional equation ...
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Stability of Quartic Functional Equations in the Spaces of Generalized Functions
... For this reason, 1.1 is called a quartic functional equation. Also Chung and Sahoo 11 determined the general solution of 1.1 without assuming any regularity conditions on the unknown function. In ...
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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 ...of quartic and quadratic functional equation between two real linear Banach ...
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Sinusoidal Time Dependent Power Series Solution to Modified Duffing Equation
... . Figure 2 displays this function in Green. Although our numeric computation applying Power Series includes “only” 14-terms its accuracy is as close as the exact solution. We further our in- vestigation applying ...
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Fuzzy approximately additive mappings
... equation with n–variables, since the function f(x) = ax is its solution. The stability problem for the generalized additive functional equation with n–variables was proved by Khodaei and Rassias ...
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On approximate dectic mappings in non-Archimedean spaces: A fixed point approach
... classical equation in the theory of functional equations is the following: ”when is it true that a function which approximately satisfies a functional equation must be close to an exact ...
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