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SUPERSTABILITY OF THE GENERALIZED PEXIDER TYPE EXPONENTIAL EQUATION IN ABELIAN GROUP
Kim, Gwang Hui The Kangwon-Kyungki Mathematical Society 2012 한국수학논문집 Vol.20 No.2
In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.
THE STABILITY OF PEXIDERIZED COSINE FUNCTIONAL EQUATIONS
Kim, Gwang Hui The Kangwon-Kyungki Mathematical Society 2008 한국수학논문집 Vol.16 No.1
In this paper, we investigate the superstability problem for the pexiderized cosine functional equations f(x+y) +f(x?y) = 2g(x)h(y), f(x + y) + g(x ? y) = 2f(x)g(y), f(x + y) + g(x ? y) = 2g(x)f(y). Consequently, we have generalized the results of stability for the cosine($d^{\prime}Alembert$) and the Wilson functional equations by J. Baker, $P.\;G{\check{a}}vruta$, R. Badora and R. Ger, and G.H. Kim.
ON THE SUPERSTABILITY OF THE PEXIDER TYPE SINE FUNCTIONAL EQUATION
Gwang Hui Kim 충청수학회 2012 충청수학회지 Vol.25 No.1
The aim of this paper is to investigate the superstabil-ity of the pexider type sine(hyperbolic sine) functional equation f(x + y)2 - (x + ¾y)2 2 2 = ¸g(x)h(y); ¸ : constant which is bounded by the unknown functions (x) or (y). As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.
일개 농촌지역 초등학교 교사와 초등학교 6학년 학생의 양성평등의식
강혜영,허광희,김유미 韓國學校保健學會 2004 韓國學校保健學會誌 Vol.17 No.2
Purpose: The purpose of this preliminary study was to investigate gender equality consciousness among elementary school teachers and the 6th graders at a rural area in Korea. Methods: There were 78 teachers and 323 6th graders from five elementary schools in Y area in Jeonnam province. The data was collected with a structured self-reported questionnaire from June to July 2003. The instrument, which was developed by Korean Women Development Institute to test gender equality consciousness, was composed of 20-items (Cronbach's α = .87 in teachr group; Cronbach's α = .83 in children group) with four subcategories: family life, school life, business life, and social life. The data was analyzed by a one-way ANOVA and t-test using SPSS/PC+. Results: 1. Teachers' gender equality consciousness: The teachers' gender equality consciousness was significantly more affirmative in females (t = 5.313, p = .001) and in the younger teacher group (F = 24.710, p = .001). On the other hand, there was no significant difference according to marital status. The differences in all four subcategories were also significantly affirmative in the female and younger teacher group. 2. Students' gender equality consciousness: The gender equality consciousness among the 6th graders was somewhat different from the teachers'. School girls (t = 8.988, p = .001) and children from double income families (t = 3.171, p = .042) were more affirmative in gender equality consciousness than the other groups. In the four sub-categories, school girls were also significantly more affirmative in all four subcategories. On the other hand, according to the family income source, the children from double income families also tended to be more affirmative only in the subcategory of family life (t = 3.196, p = .042) Conclusions: Gender equality consciousness is remarkably different according to gender both in Korean elementary school teachers and in school children. Age was a key variable in teachers for gender equality consciousness. Further research in gender equality consciousness of parents, school principals and urban school population would be useful. In order to promote gender equality consciousness, various educational materials and a mass education campaign should be developed.
Superstability of Pexiderized functional equations arising from distance measures
Kim, Gwang Hui,Lee, Young Whan International Scientific Research Publications MY 2016 The journal of nonlinear science and applications Vol.9 No.2
<P>In this paper, we obtain the superstability of the functional equation f (pr, qs) + g(ps, qr) = theta (pq, rs)h(p, q)k(r, s) for all p, q, r, s is an element of G, where G is an Abelian group, f, g, h, k are functionals on G(2), and theta is a cocycle on G(2). This functional equation is a generalized form of the functional equation f (pr, qs) + f (ps, qr) = f (p, q) f (r, s), which arises in the characterization of symmetrically compositive sum-form distance measures and the information measures, and also they can be represented as products of some multiplicative functions and the exponential functional equations. As corollaries, we obtain the superstability of the many functional equations (combination of three variables functions, for example: f (pr, qs) + g(ps, qr) = theta (pq, rs)h(p, q)g(r, s)). (C)2016 All rights reserved.</P>
A Note on Hermitian Elements of a Banach Algebra
Kim, Gwang-Hui 충청수학회 1988 충청수학회지 Vol.1 No.1
In this paper, the abelian property of Hermitian elements holds not generally in Banach algebra, but in the case that some conditions satisfy, they are abelian. By using property of [1], [2], the Hermitian elements a and b in Banach algebras have been shown that ab = ba.