• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제10권3호
• /
• pp.185-192
• /
• 2003

It is shown that every almost linear mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a linen. mapping when h(rx) = rh(x) (r > 0,$r\;{\neq}\;1$$x{\;}{\in}{\;}X$, that every almost quadratic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a quadratic mapping when $h(rx){\;}={\;}r^2h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$, and that every almost cubic mapping $h{\;}:{\;}X{\;}{\rightarrow}{\;}Y$ of a complex normed space X to a complex normed space Y is a cubic mapping when $h(rx){\;}={\;}r^3h(x){\;}(r{\;}>{\;}0,r\;{\neq}\;1)$ holds for all $x{\;}{\in}{\;}X$.

• 호남수학학술지
• /
• 제42권2호
• /
• pp.391-409
• /
• 2020

In the current paper, the intuitionistic fuzzy normed space version of Hyers-Ulam stability for multi-additive, multi-cubic and multi-additive-cubic mappings by using a fixed point method are studied. Moreover, a few corollaries corresponding to some known stability and hyperstability outcomes in intuitionistic fuzzy normed space are presented.

• Kyungpook Mathematical Journal
• /
• 제58권2호
• /
• pp.291-305
• /
• 2018

In this paper, we prove a general uniqueness theorem which is useful for proving the uniqueness of the relevant additive mapping, quadratic mapping, cubic mapping, quartic mapping, or the additive-quadratic-cubic-quartic mapping when we investigate the (generalized) Hyers-Ulam stability.

• 대한수학회논문집
• /
• 제39권1호
• /
• pp.127-135
• /
• 2024

In this paper, we improve Corollary 1 of [4] and then present an example to show that the assertion in the mentioned corollary can not be valid in the singularity case.

• 충청수학회지
• /
• 제30권2호
• /
• pp.239-249
• /
• 2017

In this paper, we approximate a fuzzy almost cubic function by a cubic function in a fuzzy sense. Indeed, we investigate solutions of the following cubic functional equation $$3f(kx+y)+3f(kx-y)-kf(x+2y)-2kf(x-y)-3k(2k^2-1)f(x)+6kf(y)=0$$. and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces.

• 대한수학회보
• /
• 제48권3호
• /
• pp.491-503
• /
• 2011

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quartic functional equation (0.1) f(2x + y) + f(2x - y) = 3f(x + y) + f(-x - y) + 3f(x - y) + f(y - x) + 18f(x) + 6f(-x) - 3f(y) - 3f(-y) in fuzzy Banach spaces.

• Korean Journal of Mathematics
• /
• 제17권3호
• /
• pp.315-330
• /
• 2009

Using the fixed point method, we prove the generalized Hyers-Ulam stability of the following cubic-quadratic functional equation $$(0.1)\;\frac{1}{2}(f(2x+y)+f(2x-y)-f(-2x-y)-f(y- 2x))\\{\hspace{35}}=2f(x+y)+2f(x-y)+4f(x)-8f(-x)-2f(y)-2f(-y)$$ in fuzzy Banach spaces.

• 충청수학회지
• /
• 제21권1호
• /
• pp.129-138
• /
• 2008

In this paper we introduce a Jensen type cubic functional equation $$f\(\frac{3x+y}{2}\)+f\(\frac{x+3y}{2}\)\\=12f\(\frac{x+y}{2}\)+2f(x)+2f(y),$$ and then investigate the generalized Hyers-Ulam stability problem for the equation.

• Kyungpook Mathematical Journal
• /
• 제60권1호
• /
• pp.133-144
• /
• 2020

We will prove the generalized Hyers-Ulam stability of cubic-quadratic-additive type functional equations and general cubic functional equations whose solutions are cubic-quadratic-additive mappings and general cubic mappings, respectively.

• East Asian mathematical journal
• /
• 제32권3호
• /
• pp.413-423
• /
• 2016

In this paper, we consider the functional equation f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 3f(y) + 3f(-y) = 0 and prove the generalized Hyers-Ulam stability for it when the target space is a fuzzy Banach space. The usual method to obtain the stability for mixed type functional equation is to split the cases according to whether the involving mappings are odd or even. In this paper, we show that the stability of a quadratic-cubic mapping can be obtained without distinguishing the two cases.