Bodaghi Abasalt
Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran.
ScientificWorldJournal. 2014 Jan 23;2014:752146. doi: 10.1155/2014/752146. eCollection 2014.
We obtain the general solution of the generalized quartic functional equation f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.
对于一个固定的正整数(m)，我们求出了广义四次函数方程(f(x + my) + f(x - my) = 2(7m - 9)(m - 1)f(x) + 2m²(m² - 1)f(y)-(m - 1)² f(2x) + m²{f(x + y) + f(x - y)})的通解。我们通过在实巴拿赫空间上的直接方法和不动点方法证明了该四次函数方程的赫尔斯 - 乌拉姆稳定性。我们还研究了上述四次函数方程在非阿基米德空间中的赫尔斯 - 乌拉姆稳定性。
