Access the full text.
Sign up today, get DeepDyve free for 14 days.
In the current work, we obtain the general solution of the following generalized cubic functional equation $$\begin{aligned}&f(x+my)+f(x-my)\\&\quad =2\left( 2\cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(x)-\frac{1}{2}\left( \cos \left( \frac{m\pi }{2}\right) +m^2-1\right) f(2x)\\&\qquad +m^2\{f(x+y)+f(x-y)\} \end{aligned}$$ f ( x + m y ) + f ( x - m y ) = 2 2 cos m π 2 + m 2 - 1 f ( x ) - 1 2 cos m π 2 + m 2 - 1 f ( 2 x ) + m 2 { f ( x + y ) + f ( x - y ) } for an integer $$m \ge 1$$ m ≥ 1 . We prove the Hyers–Ulam stability and the superstability for this cubic functional equation by the directed method and a fixed point approach. We also employ the mentioned functional equation to establish the stability of cubic Jordan $$*$$ ∗ -derivations on $$C^*$$ C ∗ -algebras and $$JC^*$$ J C ∗ -algebras.
ANNALI DELL'UNIVERSITA' DI FERRARA – Springer Journals
Published: Jul 13, 2013
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.