• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.649-662
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• 2022

This paper is concerned with the existence of solutions for a class of 𝚽-Kirchhoff type equations with critical exponent in Orlicz-Sobolev spaces. Our technical approach is based on variational methods.

• East Asian mathematical journal
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• 제25권4호
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• pp.505-516
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• 2009

In this paper, we consider a new class of generalized mixed vector equilibrium-like problems in Banach spaces. By using Fan-KKM Theorem and Nadler's Theorem, we prove the existence theorem of solution for this class of generalized mixed vector equilibrium-like problems.

• 한국실내디자인학회논문집
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• 제13권1호
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• pp.62-69
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• 2004

The purpose of this study was to analyze spatial composition of elderly skilled nursing facility and to provide basic information for setting up the detail facility architectural guidelines. The results of the study were following: the residential spaces of the facilities in this study were more or less overcrowded since their capacity were more than 5 elderly residents. The dimensions of some residential spaces did not even come up to the standard of elderly welfare law in force. On the other hand, the facilities had a tendency to use a space with multiple purposes or to allocate a space but to leave it with no use. Moreover comparing with the 1st floor, which was mainly for the staffs and had enough space to spare, the upper floor which was for the elderly residents, was crowded with nursing staffs and elderly residents and had densely closed residential and public spaces. For the problem solving, law and regulation modification is needed according to the case study about the usage and using frequency of each facility space. And the crowded area for the elderly residents could be enlarged through the reduction(or combination) of the rarely used spaces and moving a few residential spaces into the 1st floor.

• 한국실내디자인학회논문집
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• 제26권3호
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• pp.55-62
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• 2017

As recently too many local museums have been built in the whole country, most of them cannot attract enough spectators. In order to resolve this problem, it is needed for local museums to differentiate their spaces and programs related to their exhibition. Thus, the purpose of this study was to analyze the characteristics of spaces and programs of local museums from the perspective of spatial marketing to activate them, and contribute to development of local cultures. This study targeted historical public museums located in Seoul and Incheon. Through preceding research, an analysis frame was established based on the keywords related to spatial marketing, and then the characteristics of spaces and programs of local museums were analyzed based on the frame. The study results are as follows. 1) Access convenience refers to openness that public museums located in Seoul and Incheon can embrace accessible locations, points of interest, and convenient facilities easily recognized by pedestrians. 2) Symbolic formativeness is to express symbolic historical contents in the museum lobby or exhibition to show the identity of local museums. 3) Visibility is needed for direct guidance signs or spaces to let spectators know directions and locations. 4) Public concern is for spectators and local residents to participate in local museums to share and utilize their partial spaces. 5) Interactivity is to induce activation of local museums by utilizing experience exhibition contents and having spectators directly contact exhibits. 6) Interest is related to cultural festival programs of exhibition to arouse spectators' and local residents' curiosity. 7) Participation is to activate spaces and spectators by providing educational programs. 8) Usefulness is to induce spectators' interest in local museums by providing historical, social, and cultural information. These results are expected to be used as baseline data to suggest a new direction for activation of local museums from the perspective of spatial marketing.

• 한국주거학회논문집
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• 제21권4호
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• pp.99-109
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• 2010

The purpose of this study is to provide basic data needed for planning apartment community spaces in order to vitalize rental apartments. Indoor community spaces of 12 rental apartments in Seoul and Kyunggi were examined. The results are as follows. First, the layout types of indoor community spaces in rental apartment complexes were found out to be mostly the building type planned in the piloties of the apartment, or the singular type placed in a singular building. Depending on the layout type, the spaces were mostly concentrated at the outskirt of the complex or the in-between space of the main building, thus lowering their recognition. Thereby, they were not satisfactory for utilization of the spaces and association of residents. Second, Indoor community space legal establishment standard and square measure did not reflect resident's feature except elderly spaces, and there was problem in activation of space. Third, as for the spatial planning of indoor community space, although each space was categorized by the users' age, the furniture and appliance planning considering users was not satisfactory. The area calculation by the type of space did not reflect the users' characteristics, thus causing problems in using the facilities. Fourth, as for the management and programs of the indoor community space, spaces were managed after categorized by the major user classes such as children, seniors, and adolescents. Depending on eagerness of program managers of each apartment complex, the level of program management varied. The survey results showed that, in most cases, almost no programs were used or merely basic management and programs were being provided.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.585-598
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• 2014

In this paper we consider the nonlinear parabolic problems with mixed boundary condition. Under comparatively mild conditions of the coefficients related to the problem, we construct the discontinuous Galerkin approximation of the solution to the nonlinear parabolic problem. We discretize spatial variables and construct the finite element spaces consisting of discontinuous piecewise polynomials of which the semidiscrete approximations are composed. We present the proof of the convergence of the semidiscrete approximations in $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ normed spaces.

• 대한수학회지
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• 제55권4호
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• pp.849-875
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• 2018

The purpose of this paper is to present an operator method of regularization for the problem of finding a solution of a system of nonlinear ill-posed equations with a monotone hemicontinuous mapping and N inverse-strongly monotone mappings in Banach spaces. A regularization parameter choice is given and convergence rate of the regularized solutions is estimated. We also give the convergence and convergence rate for regularized solutions in connection with the finite-dimensional approximation. An iterative regularization method of zero order in a real Hilbert space and two examples of numerical expressions are also given to illustrate the effectiveness of the proposed methods.

• 대한수학회보
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• 제56권3호
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.59-82
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• 2022

In this paper, we present a modified (improved) generalized M-iteration with the inertial technique for three quasi-nonexpansive multivalued mappings in a real Hilbert space. In addition, we obtain a weak convergence result under suitable conditions and the strong convergence result is achieved using the hybrid projection method with our modified generalized M-iteration. Finally, we apply our convergence results to certain optimization problem, and present some numerical experiments to show the efficiency and applicability of the proposed method in comparison with other improved iterative methods (modified SP-iterative scheme) in the literature. The results obtained in this paper extend, generalize and improve several results in this direction.

• Kyungpook Mathematical Journal
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• 제63권3호
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• pp.437-450
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• 2023

In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations with a new class of multipoint and nonlocal integral boundary conditions. We define a 𝓩^*_λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.