• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.

• Korean Journal of Mathematics
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• v.21 no.3
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• pp.325-330
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• 2013

In this paper, we prove Trotter-Kato theorem in the weak topology if $X^*$ is a uniformly convex Banach space.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.5
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• pp.1-4
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• 1998

The main goal of this paper is to investigate some properties of the locally convex fuzzy topological vector space.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.129-140
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• 2002

In this paper, we obtain a strong law of large numbers for convex tight random elements taking values in the space of fuzzy numbers in R.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1311-1332
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• 2013

This paper concerns the evolution of a closed hypersurface of the hyperbolic space, convex by horospheres, in direction of its inner unit normal vector, where the speed equals a positive power ${\beta}$ of the positive mean curvature. It is shown that the flow exists on a finite maximal interval, convexity by horospheres is preserved and the hypersurfaces shrink down to a single point as the final time is approached.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.665-678
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• 2022

The aim of this paper is to introduce a new iterative process and show that our iteration scheme is faster than other existing iteration schemes with the help of numerical examples. Next, we have established convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some convergence results for the approximation of the fixed points of a nonexpansive mapping.

• KIEAE Journal
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• v.11 no.6
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• pp.95-100
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• 2011

Although Space Syntax is a well-known technique for spatial analysis, debates have taken place among some researchers because the Space Syntax discards geometric information as both shapes and sizes of spaces, and hence may cause some inconsistencies. Therefore, this study aims at developing methods to recognize and manage spatial shapes for more precise space syntax analysis. To reach this goal, this study employed both a graph theory and binary spatial partitioning (BSP) tree to recognize and manage spatial information. As a result, spatial shapes and sizes could be recognized by checking loops in graph converted from spatial shapes of built environment. Each spatial shape could be managed sequentially by BSP tree with hierarchical structure. Through such recognition and management processes, convex maps composed of the fattest and fewest convex spaces could be drawn. In conclusion, we hope that the methods developed here will be useful for urban planning to find appropriate purposes of spaces to satisfy the sustainability of built environment on the basis of the spatial and social relationships in urban spaces.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.185-197
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• 2015

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(f_n)-Lipschitzian map- pings and an infinite family of g_n-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

• KIEAE Journal
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• v.10 no.3
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• pp.57-62
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• 2010

To effectively use Building Information Modelling (BIM) dealing with semantic information including the entities of building components, the information about building components should be standardized. Like standardized modern buildings. in the past, Korean traditional houses were built according to strict procedures and formats. Therefore, if the Korean traditional house are modelled by using BIM,. not only the Korean traditional house of good quality will be built quickly and cheaply, but also spaces in the existing Korean traditional house will be easily analyzed. However, when analyzing spaces of the Korean traditional house using Space Syntax, some problems are caused in dividing outdoor space such as yard with unclear boundaries, unlike indoor space with clear boundaries surrounded by walls. These comes from the fact that researchers have subjectively divided a space in the house into convex spaces as units for Space Syntax analysis. Therefore, this study aims to develop an objective and rational spatial subdivision technique for Space Syntax analysis of a Korean traditional house modelled by using BIM. We could objectively and reasonably divide a Korean traditional house space into convex spaces by recognizing the building components in the house modelled in the form of Industry Foundation Classes(IFC). Depending on the connection of convex spaces allocated in the spatial subdivision technique, j-graph in Space Syntax could be drawn and the measurements of spatial configurations could be determinded. Through the developed technique, the social properties including the cultural and philosophical aspects of Korean people was identified by measuring the spatial configurations of Korean traditional house. The developed technique will serve as useful means to help architects to find an appropriate purpose of each space for sustainable architecture on the basis of the spatial and social relationships in buildings or urban systems.