• Journal of applied mathematics & informatics
• /
• 제9권1호
• /
• pp.371-380
• /
• 2002

In this paper we obtain the general solution of a quadratic Jensen type functional equation : (equation omitted) and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• 대한수학회보
• /
• 제45권1호
• /
• pp.111-118
• /
• 2008

Using the Hyers-Ulam-Rassias stability method, we investigate isomorphisms in quasi-Banach algebras and derivations on quasi-Banach 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 in [2, 17]. The concept of Hyers-Ulam-Rassias stability originated from the Th. M. Rassias' stability theorem that appeared in the paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Furthermore, isometries and isometric isomorphisms in quasi-Banach algebras are studied.

• 충청수학회지
• /
• 제19권2호
• /
• pp.159-175
• /
• 2006

This paper is a survey on the Hyers-Ulam-Rassias stability of the Jensen functional equation in $C^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Its content is divided into the following sections: 1. Introduction and preliminaries. 2. Approximate isomorphisms in $C^*$-algebras. 3. Approximate isomorphisms in Lie $C^*$-algebras. 4. Approximate isomorphisms in $JC^*$-algebras. 5. Stability of derivations on a $C^*$-algebra. 6. Stability of derivations on a Lie $C^*$-algebra. 7. Stability of derivations on a $JC^*$-algebra.

• 충청수학회지
• /
• 제19권3호
• /
• pp.245-261
• /
• 2006

In this paper, we prove the generalized Hyers-Ulam stability of ring homomorphisms over the p-adic field $\mathbb{Q}_p$ associated with the Cauchy functional equation f(x+y) = f(x)+f(y) and the Cauchy-Jensen functional equation $2f(\frac{x+y}{2}+z)=f(x)+f(y)+2f(z)$.

• 충청수학회지
• /
• 제23권2호
• /
• pp.335-348
• /
• 2010

In this paper, we study the Hyers-Ulam-Rassias stability of a bi-Pexider functional equation $$f(x+y,z)-f_1(x,z)-f_2(y,z)=0$$, $$f(x,y+z)-f_3(x,y)-f_4(x,z)=0$$. Moreover, we establish stability results on the punctured domain.

• 한국가스학회지
• /
• 제22권1호
• /
• pp.64-77
• /
• 2018

Horseshoe Canyon 석탄층 메탄가스 광구 4개 생산정의 생산이력과 압력 시험자료를 바탕으로 물질평형법과 감퇴곡선법을 이용하여 원시부존량을 예측하는 연구를 수행하였다. 물질평형법은 전통가스 물질평형법과 Jensen and Smith법을 이용하였고, 감퇴곡선법은 Arps 경험식과 Khaled 법을 이용하였다. 그 결과, 전통가스 물질평형법과 Jensen and Smith법을 이용한 경우의 차이는 12% 이내로 부존량 예측에 큰 차이는 없고, 감퇴곡선법을 적용한 경우, 감퇴지수가 1이상, 최대 3.5에 이르러, Arps 방정식을 이용하면 부존량이 무한대로 산출되므로 Khaled 법을 적용하는 것이 적절하였다. 전통가스 물질평형방정식을 이용한 부존량 예측 결과와 Khaled 법을 이용한 예측 결과의 차이는 8.67% ~ 31.04% 였고, Jensen and Smith 방정식과 Khaled 법을 이용한 부존량 예측 결과의 차이는 13.67% ~ 26.49%로 후자의 경우가 차이가 더 적었다.

• 충청수학회지
• /
• 제15권1호
• /
• pp.25-33
• /
• 2002

We prove the generalized Hyers-Ulam-Rassias stability of linear operators in a Hilbert module over a unital $C^*$-algebra.

• 충청수학회지
• /
• 제24권2호
• /
• pp.371-381
• /
• 2011

We establish alternative stability and superstability of $J^{\ast}$-derivations in $J^{\ast}$-algebras for a generalized Jensen type functional equation by using the direct method and the fixed point alternative method.

• 충청수학회지
• /
• 제21권1호
• /
• pp.1-14
• /
• 2008

In this paper, we prove the Hyers-Ulam-Rassias stability of the Cauchy functional equation f(x+y) = f(x)+f(y) and of the Jensen functional equation $2f(\frac{x+y}{2})=f(x)+f(y)$ over the p-adic field ${\mathbb{Q}}_p$. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• 충청수학회지
• /
• 제21권4호
• /
• pp.455-466
• /
• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.