• Korean Journal of Mathematics
• /
• v.22 no.4
• /
• pp.659-670
• /
• 2014

In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.

• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.4
• /
• pp.467-476
• /
• 2017

In this paper, we obtain the stability of the additive-quadratic functional equation f(x+y, z+w)+f(x+y, z-w) = 2f(x, z)+2f(x, w)+2f(y, z)+2f(y, w) and the bi-Jensen functional equation $$4f(\frac{x+y}{2},\;\frac{z+w}{2})=f(x,\;z)+f(x,\;w)+f(y,\;z)+f(y,\;w)$$ in 2-Banach spaces.

• The Pure and Applied Mathematics
• /
• v.18 no.2
• /
• pp.161-172
• /
• 2011

In this paper we investigate the Hyers-Ulam stability of a Jensen type functional equation in multi-normed spaces and then extend the result to multi-normed left modules over a normed algebra A.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.269-277
• /
• 2007

It is shown that $f:\mathbb{R}{\rightarrow}\mathbb{R}$ satisfies the following functional inequalities (0.1) ${\mid}f(x)+f(y){\mid}{\leq}{\mid}f(x+y){\mid}$, (0.2) ${\mid}f(x)+f(y){\mid}{\leq}{\mid}2f(\frac{x+y}{2}){\mid}$, (0.3) ${\mid}f(x)+f(y)-2f(\frac{x-y}{2}){\mid}{\leq}{\mid}2f(\frac{x+y}{2}){\mid}$, respectively, then the function $f:\mathbb{R}{\rightarrow}\mathbb{R}$ satisfies the Cauchy functional equation, the Jensen functional equation and the Jensen quadratic functional equation, respectively.

• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.397-411
• /
• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.3
• /
• pp.361-370
• /
• 2008

We consider the Hyers-Ulam type stability of the Cauchy, Jensen, Pexider, Pexider-Jensen differences: $$(0.1){\hspace{55}}C(u):=u{\circ}A-u{\circ}P_1-u{\circ}P_2,\\(0.2){\hspace{55}}J(u):=2u{\circ}\frac{A}{2}-u{\circ}P_1-u{\circ}P_2,\\(0.3){\hspace{18}}P(u,v,w):=u{\circ}A-v{\circ}P_1-w{\circ}P_2,\\(0.4)\;JP(u,v,w):=2u{\circ}\frac{A}{2}-v{\circ}P_1-w{\circ}P_2$$, with respect to bounded distributions.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.645-656
• /
• 2009

J. Wang [21] proposed a problem: whether the Hyers-Ulam-Rassias stability of Jensen's equation for the case p, q, r, s $\in$ ($\beta$, $\frac{1}{\beta}$) \ {1} holds or not under the assumption that G and E are $\beta$-homogeneous Fspace (0 < $\beta\;\leq$ 1). The main purpose of this paper is to give an answer to Wang's problem. Furthermore, we proved that the stability property of Jensen's equation is not true as long as p or q is equal to $\beta$, $\frac{1}{\beta}$, or $\frac{\beta_2}{\beta_1}$ (0 < $\beta_1,\beta_2\leq$ 1).

• Korean Journal of Mathematics
• /
• v.17 no.1
• /
• pp.83-90
• /
• 2009

In this paper, we investigate isomorphisms between $C^*$-ternary algebras and derivations on $C^*$-ternary algebras associated with the Cauchy-Jensen functional equation $$2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$$, which was introduced and investigated by Baak in [2].

• The Pure and Applied Mathematics
• /
• v.26 no.4
• /
• pp.305-313
• /
• 2019

Using the fixed point method, we prove the Hyers-Ulam stability of 3-Lie homomorphisms and 3-Lie derivations in 3-Lie algebras for Cauchy-Jensen functional equation.

• The Pure and Applied Mathematics
• /
• v.22 no.4
• /
• pp.343-357
• /
• 2015

Using the fixed point method, we prove the Hyers-Ulam stability of lin- ear mappings in Banach modules over a unital C*-algebra and in non-Archimedean Banach modules over a unital C*-algebra associated with the orthogonally Cauchy- Jensen additive functional equation.