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On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces  [cached]
Gordji MEshaghi,Abbaszadeh S,Park Choonkil
Journal of Inequalities and Applications , 2009,
Abstract: We establish the general solution of the functional equation for fixed integers with and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.
On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces
M. Eshaghi Gordji,S. Abbaszadeh,Choonkil Park
Journal of Inequalities and Applications , 2009, DOI: 10.1155/2009/153084
Abstract: We establish the general solution of the functional equation f(nx+y)+f(nx y)=n2f(x+y)+n2f(x y)+2(f(nx) n2f(x)) 2(n2 1)f(y) for fixed integers n with n≠0,±1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.
On the stability of generalized mixed type quadratic and quartic functional equation in quasi-Banach spaces  [PDF]
S. Abbaszadeh,M. Eshaghi Gordji
Mathematics , 2008,
Abstract: In this paper, we establish the general solution of the functional equation $$f(nx+y)+f(nx-y)=n^2f(x+y)+n^2f(x-y)+2(f(nx)-n^2f(x))-2(n^2-1)f(y)\eqno {0 cm}$$for fixed integers $n$ with $n\neq0,\pm1$ and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.
On the Stability of Generalized Quartic Mappings in Quasi- -Normed Spaces  [cached]
Kang Dongseung
Journal of Inequalities and Applications , 2010,
Abstract: We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi- -normed spaces and then the stability by using a subadditive function for the generalized quartic function such that , where , , , for all .
Stability of an Additive-Cubic-Quartic Functional Equation  [cached]
Eshaghi-Gordji M,Kaboli-Gharetapeh S,Park Choonkil,Zolfaghari Somayyeh
Advances in Difference Equations , 2009,
Abstract: In this paper, we consider the additive-cubic-quartic functional equation and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces.
Stability of cubic and quartic functional equations in non-Archimedean spaces  [PDF]
M. Eshaghi Gordji,M. Bavand Savadkouhi
Mathematics , 2008,
Abstract: We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation $f(kx+y)+f(kx-y)=k[f(x+y)+f(x-y)]+2(k^3-k)f(x)$ for all $k\in \Bbb N$ and the quartic functional equation $f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$ for all $k\in \Bbb N$ in non-Archimedean normed spaces.
Random Stability of an Additive-Quadratic-Quartic Functional Equation  [cached]
Mohamadi M,Cho YJ,Park C,Vetro P
Journal of Inequalities and Applications , 2010,
Abstract: Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation in complete random normed spaces.
Fuzzy Stability of an Additive-Quadratic-Quartic Functional Equation  [cached]
Park Choonkil
Journal of Inequalities and Applications , 2010,
Abstract: Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-quartic functional equation: in fuzzy Banach spaces.
Stability of an Additive-Cubic-Quartic Functional Equation in Multi-Banach Spaces  [PDF]
Zhihua Wang,Xiaopei Li,Themistocles M. Rassias
Abstract and Applied Analysis , 2011, DOI: 10.1155/2011/536520
Abstract: We prove the Hyers-Ulam stability of the additive-cubic-quartic functional equation in multi-Banach spaces by using the fixed point alternative method. The first results on the stability in the multi-Banach spaces were presented in (Dales and Moslehian 2007). 1. Introduction Stability is investigated when one is asking whether a small error of parameters in one problem causes a large deviation of its solution. Given an approximate homomorphism, is it possible to approximate it by a true homomorphism? In other words, we are looking for situations when the homomorphisms are stable, that is, if a mapping is almost a homomorphism, then there exists a true homomorphism near it with small error as much as possible. This problem was posed by Ulam in 1940 (cf. [1]) and is called the stability of functional equations. For Banach spaces, the problem was solved by Hyers [2] in the case of approximately additive mappings. Later, Hyers' result was generalized by Aoki [3] for additive mappings and by Rassias [4] for linear mappings by allowing the Cauchy difference to be unbounded. During the last decade, stability of functional equations was studied by several mathematicians for mappings in various spaces including random normed spaces and fuzzy Banach spaces (cf. [5, 6]). For various other results on the stability of functional equations, one is referred to [7–26]. Most of the proofs of stability theorems in the Hyers-Ulam context have applied Hyers’ direct method. The exact solution of the functional equation is explicitly constructed as the limit of a sequence, which is originating from the given approximate solution. In 2003, Radu [27] proposed the fixed point alternative method for obtaining the existence of exact solutions and error estimations and noticed that a fixed point alternative method is essential for the solution of Ulam problem for approximate homomorphisms. Subsequently, some authors [28, 29] applied the fixed alternative method to investigate the stability problems of several functional equations. The notion of multi-normed space was introduced by Dales and Polyakov [30] (or see [31, 32]). This concept is somewhat similar to operator sequence space and has some connections with operator spaces and Banach lattices. Motivations for the study of multi-normed spaces and many examples were given in [30, 31]. In 2007, stability of mappings on multi-normed spaces was first given in [31], and asymptotic aspect of the quadratic functional equation in multi-normed spaces was investigated in [33]. In this paper, we consider the following functional equation
Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces  [PDF]
M. Eshaghi Gordji,S. Zolfaghari,J. M. Rassias,M. B. Savadkouhi
Abstract and Applied Analysis , 2009, DOI: 10.1155/2009/417473
Abstract: We obtain the general solution and the generalized Ulam-Hyers stability of the mixed type cubic and quartic functional equation (
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