• Honam Mathematical Journal
• /
• v.34 no.1
• /
• pp.19-34
• /
• 2012

In this paper, we investigate the stability of a functional equation f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z) = 0 by using the fixed point theory in the sense of L. Cadariu and V. Radu.

• Journal of the Chungcheong Mathematical Society
• /
• v.28 no.3
• /
• pp.353-363
• /
• 2015

In this paper, we investigate the functional equation f(3x+y)+f(3x-y) = f(x+2y)+2f(x-y)+6f(2x)+3f(x)-6f(y) and prove the generalized Hyers-Ulam stability for it in non-Archimedean normed spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.535-542
• /
• 2007

In this paper, we investigate the generalized Hyers-Ulam{Rasssias stability of the following Euler-Lagrange type quadratic functional equation $$f(ax+by+cz)+f(ax+by-cz)+f(ax-by+cz)+f(ax-by-cz)=4a^2f(x)+4b^2f(y)+4c^2f(z)$$.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.4
• /
• pp.657-661
• /
• 2016

Let $f:X{\rightarrow}X$ be a continuous surjection of a compact metric space and let ($X_f,{\tilde{f}}$) be the inverse limit of a continuous surjection f on X. We show that for a continuous surjective map f, if f has the asymptotic average, the average shadowing, the ergodic shadowing property then ${\tilde{f}}$ is topologically transitive.

• East Asian mathematical journal
• /
• v.34 no.5
• /
• pp.693-702
• /
• 2018

In this paper, we consider the generalized Hyers-Ulam stability for the following additive-quadratic functional equation with involution $f(x+2y)-f(2x+y)+f(x+y)+f({\sigma}(x)+y)+f(x)-4f(y)-f({\sigma}(y))=0$ in non-Archimedean spaces.

• The Pure and Applied Mathematics
• /
• v.26 no.4
• /
• pp.267-276
• /
• 2019

In this paper, we investigate the stability of an additive-cubic-quartic functional equation f(x + 2y) - 4f(x + y) + 6f(x) - 4f(x - y) + f(x - 2y) - 12f(y) - 12f(-y) = 0 by applying the fixed point theory in the sense of L. Cădariu and V. Radu.

• The Pure and Applied Mathematics
• /
• v.26 no.4
• /
• pp.247-254
• /
• 2019

In this paper, we investigate Hyers-Ulam-Rassias stability of the functional equation f(x + ky) - k²f(x + y) + 2(k² - 1)f(x) - k²f(x - y) + f(x - ky) - k²(k² - 1)(f(y) + f(-y)) = 0, where k is a fixed real number with |k| ≠ 0, 1.

• The Pure and Applied Mathematics
• /
• v.19 no.1
• /
• pp.59-71
• /
• 2012

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation $$f(x+y+z)-f(x+y)-f(y+z)-f(x+z)+f(x)+f(y)+f(z)=0$$. by using a fixed point theorem in the sense of L. C$\breve{a}$dariu and V. Radu.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.561-567
• /
• 2001

In this paper, we investigate the Hyers-Ulam-Rassias stability of a quadratic functional equation f(x+y+z)+f(x-y)+f(y-z)+f(x-z) = 3f(x)+3f(y)+3f(z) and prove the Hyers-Ulam stability of the equation on bounded domains.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.29-38
• /
• 2016

For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.