• 충청수학회지
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• 제33권3호
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• pp.319-326
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• 2020

In this paper, we establish a general solution of the following functional equation $$mf\({\sum\limits_{k=1}^{n}}x_k\)+{\sum\limits_{t=1}^{m}}f\({\sum\limits_{k=1}^{n-i_t}}x_k-{\sum\limits_{k=n-i_t+1}^{n}}x_k\)=2{\sum\limits_{t=1}^{m}}\(f\({\sum\limits_{k=1}^{n-i_t}}x_k\)+f\({\sum\limits_{k=n-i_t+1}^{n}}x_k\)\)$$ where m, n, t, i_t ∈ ℕ such that 1 ≤ t ≤ m < n. Also, we study Hyers-Ulam-Rassias stability for the generalized quadratic functional equation with n-variables and m-combinations form in quasi-𝛽-normed spaces and then we investigate its application.

• 한국실내디자인학회논문집
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• 제26권5호
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• pp.143-151
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• 2017

This study aims to analyze the design of public libraries which act as anchors in culture-led urban regeneration. They have been built as city's symbols as well as catalysts to revitalize city centers and urban spaces since the 1990s. This study finds that the public libraries play roles in the urban development as cultural icons, multi-functional spaces, and public domain. This study examines the five examples of the libraries and finds their important design qualities as follow. First, public libraries are planned to symbolize local culture and history as cultural icons. The shapes of public libraries are expressed with sculptured cultural icons, while their facades are designed to signify cities' identities and images. Second, public libraries in culture-led urban regeneration have multi-functional spaces which provide diverse activities and experiences to visitors. The libraries often have galleries and theaters for cultural life, cafes and shops for daily uses, educational facilities, as well as public services, parking, and transport systems that connect to urban infrastructure. Third, the public libraries become the anchors of surrounding public spaces and cultural buildings. The libraries have the sequences of approach from entry plazas, transitional zones, and entrances to lobbies. Especially the transitional zones between the libraries and the cities that are covered with giant cantilevers expand the libraries' space and establish attractive urban spaces. Forth, the libraries employ nature and cityscapes in their design. The surfaces and openings of the libraries are adjusted to allow many attractive views to visitors. Fifth, the libraries have big lobby spaces which are the centers of the buildings as well as the public domain. The lobby spaces are designed as in-door spaces like out-doors with vertical and horizontal openness that allow the natural flows of light from ceilings, glass walls and vertical voids.

• 충청수학회지
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• 제20권4호
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• pp.515-523
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• 2007

In this paper, we investigate the Hyers-Ulam-Rassias stability of generalized Jensen type quadratic functional equations in Banach spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.365-374
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• 2015

In this paper, we solve the additive ρ-functional equations

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.375-382
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• 2015

In this paper, we solve the additive ρ-functional equations

• 대한수학회보
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• 제46권1호
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• pp.87-97
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• 2009

We prove the Hyers-Ulam stability of the sine and cosine functional equations in the spaces of generalized functions such as Schwartz distributions, Fourier hyperfunctions, and Gelfand generalized functions.

• East Asian mathematical journal
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• 제35권3호
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• pp.331-340
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• 2019

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

• 충청수학회지
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• 제35권2호
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• pp.149-159
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• 2022

In this note, we prove some theorems concerning the stability of functional inequality associated with additive mappings on quasi-𝛽-normed spaces.

• 의료ㆍ복지 건축 : 한국의료복지건축학회 논문집
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• 제7권1호
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• pp.7-14
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• 2001

The purpose of this study is to suggest the improvement directions and conditions of spacial composition according to location style of silver towns. The spacial composition of silver town used in 3 cases are analyzed according to their location(the urban type, the sub-urban type and the resort type). The points of analysis are focused on the necessary spaces and selectable spaces related to location of silver towns. In conclusion, the urban and sub-urban silver towns should have the necessary spaces and selectable spaces through analysis of the spaces in healthcare facilities near at hand. The resort silver towns should be planned to harmony the functional spaces with building shapes because they consist of various spaces.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.971-983
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• 2021

In this paper, we prove common fixed point theorems for six weakly compatible mappings in G-fuzzy metric spaces introduced by Sun and Yang [16] which is actually generalization of G-metric spaces. G-metric spaces coined by Mustafa and Sims [13]. The paper concerns our sustained efforts for the materialization of G-fuzzy metric spaces and their properties. We also exercise the concept of symmetric G-fuzzy metric space, 𝜙-function and weakly compatible mappings. The results present in this paper generalize the well-known comparable results in the literature. We justify our results by suitable examples. Some applications are also given in support of our results.