• International Journal of High-Rise Buildings
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• v.12 no.3
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• pp.251-262
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• 2023

In response to China's "Regulations on the Management of Earthquake Resistance of Building Constructions" on the provision of eight types of important buildings to maintain functional after fortified earthquakes occur, "Guidelines for Seismic Design of post-quake functional buildings (Draft for Review)" distinguishes Class I and Class II buildings, and gives the performance objectives and seismic verification requirements for design earthquakes and severe earthquakes respectively. In this paper, a hospital and a school building are selected as examples to design according to the requirements of fortification of Intensity 8 and 7 respectively. Two design strategies, the seismic isolation scheme and energy dissipation scheme, are considered which are evaluated through elastic-plastic dynamic time-history analysis to meet the requirement of post-quake functional buildings. The results show that the seismic isolation design can meet the requirements in the above cases, and the energy dissipation scheme is difficult to meet the requirements of the "Guidelines" on floor acceleration in some cases, for which the scheme shall be made valid through the seismic resilience assessment. The research in this paper can provide a reference for designers to choose schemes for post-quake functional buildings.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.409-421
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• 2012

In this paper, using an efficient change of variables we refine the Hyers-Ulam stability of the alternative Jensen functional equations of J. M. Rassias and M. J. Rassias and obtain much better bounds and remove some unnecessary conditions imposed in the previous result. Also, viewing the fundamentals of what our method works, we establish an abstract version of the result and consider the functional equations defined in restricted domains of a group and prove their stabilities.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.109-115
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• 2007

In this paper, we obtain the general solution and the stability of the multi-dimensional Cauchy's functional equation $f(x_1+y_1,{\cdots},x_n+y_n)=f(x_1,{\cdots},x_n)+f(y_1,{\cdots},y_n)$. The function f given by $f(x_1,{\cdots},x_n)=a_1x_1+{\cdots}+a_nx_n$ is a solution of the above functional equation.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.377-384
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• 2008

In this paper, we prove the stability of the functional equation $$\sum\limits_{i=0}^{3}3Ci(-1)^{3-i}f(ix+y)-3!f(x)=0$$ in the sense of P. $G{\breve{a}}vruta$ on the punctured domain. Also, we investigate the superstability of the functional equation.

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

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.57-73
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• 2005

In this paper we solve a generalized quadratic Jensen type functional equation $m^2 f (\frac{x+y+z}{m}) + f(x) + f(y) + f(z) =n^2 [f(\frac{x+y}{n}) +f(\frac{y+z}{n}) +f(\frac{z+x}{n})]$ and prove the stability of this equation in the spirit of Hyers, Ulam, Rassias, and Gavruta.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.525-537
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• 2020

In this paper, we introduce a duotrigintic functional equation. Furthermore, we study the Hyers-Ulam stability of a duotrigintic functional equation in Banach spaces by using the direct method.

• Korean Journal of Mathematics
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• v.16 no.1
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• pp.103-114
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• 2008

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.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.159-168
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• 2020

In this paper, we investigate Hyers-Ulam-Rassias stability of a functional equation f(x + ky) + f(x - ky) - k²f(x + y) - k²f(x - y) + 2(k² - 1)f(x) + (k² + k³)f(y) + (k² - k³)f(-y) - 2f(ky) = 0.