# Solution and Stability of a Mixed Type Cubic and Quartic Functional Equation in Quasi-Banach Spaces

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- Stability of Mixed Type Cubic and Quartic Functional Equations in Random Normed Spaces. Gordji, M. Eshaghi; Savadkouhi, M. B. // Journal of Inequalities & Applications;2009, Vol. 2009, Special section p1
We obtain the stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms f(x + 2y) + f(x - 2y) = 4[f(x + y) + f(x - y)] - 24f(y) - 6f(x) + 3f(2y).

- Stability of an Additive-Cubic-Quartic Functional Equation in Multi-Banach Spaces. Zhihua Wang; Xiaopei Li; Rassias, Themistocles M. // Abstract & Applied Analysis;2011, Special section p1
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).

- GENERALIZED HYERS-ULAM STABILITY OF AN AQCQ-FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN BANACH SPACES. Choonkil Park; Gordji, Madjid Eshaghi; Najati, Abbas // Journal of Nonlinear Sciences & its Applications;2010, Vol. 3 Issue 4, p272
In this paper, we prove the generalized Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x - 2y) = 4f(x + y) + 4f(x - y) - 6f(x) + f(2y) + f(-2y) - 4f(y) - 4f(-y) in non-Archimedean Banach spaces.

- On the Stability of Generalized Quartic Mappings in Quasi-Î²-Normed Spaces. Dongseung Kang // Journal of Inequalities & Applications;2010, Vol. 2010, p1
We investigate the generalized Hyers-Ulam-Rassias stability problem in quasi-Î²-normed spaces and then the stability by using a subadditive function for the generalized quartic function f : X â†’ Y such that f(ax+by)+f(ax-by)-2a2(a2 -b2)f(x) = (ab)2[f(x+y)+f(x-y)]-2b2(a2 -b2)f(y), where...

- On the Generalized Hyers-Ulam-Rassias Stability for a Functional Equation of Two Types in p-Banach Spaces. Kyoo-Hong Park; Yong-Soo Jung // Kyungpook Mathematical Journal;2008, Vol. 48 Issue 1, p45
We investigate the generalized Hyers-Ulam-Rassias stability in p-Banach spaces for the following functional equation which is two types, that is, either cubic or quadratic: 2f(x + 3y) + 6f(x - y) + 12f(2y) = 2f(x - 3y) + 6f(x + y) + 3f(4y). The concept of Hyers-Ulam-Rassias stability originated...

- Solution and Stability of a General Mixed Type Cubic and Quartic Functional Equation. Xiaopeng Zhao; Xiuzhong Yang; Chin-Tzong Pang // Journal of Function Spaces & Applications;2013, p1
We consider the following mixed type cubic and quartic functional equation Î»[f(x + Î»y) + f(x - Î»y)] = Î»Â³[f(x + y) + f(x - y)] - 2Î»Â³(Î» + 1)f(Î»y) - 2Î»(Î»Â² - 1)f(x) + 2(Î» + 1)f(Î»y), where Î» is a fixed integer. We establish the general solution of the...

- On the Stability of Functional Equations in Random Normed spaces. Chugh, Renu // International Journal of Computer Applications;May2012, Vol. 45, p25
Let Æ’ be a mapping from a linear space X into a complete Random Normed Space Y. In this paper, we prove some results for the stability of Cubic, Quadratic and Jensen-Type Quadratic functional equations in the setting of Random Normed Spaces (RNS).

- On the Stability of a Generalized Quadratic and Quartic Type Functional Equation in Quasi-Banach Spaces. Gordji, M. Eshaghi; Abbaszadeh, S.; Park, Choonkil // Journal of Inequalities & Applications;2009, Vol. 2009, Special section p1
We establish the general solution of the functional equation f(nx + y) + f(nx + y) = n2f(nx - y) + n2 f(x - y) + 2(f(nx) - n2f(x)) - 2(n2 - 1)f(y) for fixed integers n with nâ‰ 0, Â±1 and investigate the generalized Hyers-Ulam stability of this equation in quasi-Banach spaces.

- Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces. Gordji, M. Eshaghi; Khodaei, H.; Hark-Mahn Kim // International Journal of Mathematics & Mathematical Sciences;2011, p1
We establish the general solution for a mixed type functional equation of aquartic and a quadratic mapping in linear spaces. In addition, we investigate the generalized Hyers-Ulam stability in p- Banach spaces.