• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1299-1316
• /
• 2010

We derive estimates for the truncation, amplitude and jitter type errors associated with Hermite-type interpolations at equidistant nodes of functions in Paley-Wiener spaces. We give pointwise and uniform estimates. Some examples and comparisons which indicate that applying Hermite interpolations would improve the methods that use the classical sampling theorem are given.

• Kyungpook Mathematical Journal
• /
• v.45 no.3
• /
• pp.433-443
• /
• 2005

In 1994, Lim-Xu asked whether the Maluta's constant D(X) < 1 implies the fixed point property for asymptotically nonexpansive mappings and gave a partial solution for this question under an additional assumption for T, i.e., weakly asymptotic regularity of T. In this paper, we shall prove that the result due to Lim-Xu is also satisfied for more general non-Lipschitzian mappings in reflexive Banach spaces with weak uniform normal structure. Some applications of this result are also added.

• Kyungpook Mathematical Journal
• /
• v.63 no.1
• /
• pp.61-78
• /
• 2023

In this paper, we introduce two new geometric constants related to the heights of triangles: ∆_H(X) and ∆_h(X, I). We also propose two new geometric constants, ∆_m(X) and ∆_M(X), related to the midlines of equilateral triangles, and discuss the relation between the heights and midlines in equilateral triangles. We give estimates for these geometric constants in terms of other geometric parameters, and the geometric constants are used to discuss geometric properties such as uniform non-squareness, uniform normal structure, and the fixed point property.

• Korean Institute of Interior Design Journal
• /
• v.16 no.3 s.62
• /
• pp.38-45
• /
• 2007

In the architectural space of modem age, expanding to the vertical and horizontal direction for the interaction between space and space is becoming an indispensable factor, and in this expansion, ramps are being positioned as one of the important factors. With an increased use of ramps, they show a variety of changes in types, functions and even concepts. The space where modem ramps are used exhibits a phenomenon that accommodates and expands many functions as well as the confined function of moving people, and is widening the scope of recognition on the functions of ramp. In addition, this phenomenon can be seen as an architectural reflection on the complexation trend of the modem society, the components comprising a ramp contact the body of experiencers closely and thus have a direct effect on their behavior or feeling, and owing to this, it is a space where new functions and meaning are highly likely to be derived. In this study, spaces where ramps are used stay away from an element of uniform vertical movement but have an independent environment within the entire space, thereby being used as a space dominating the nature of the building, not a subsidiary element of it. In this study, therefore, it could be known that spaces in which ramps are used are different in their meaning according to the patterns, not as an element of uniform vertical movement. In addition, these conclusions are the results by analyzing the patterns of ramps taking place in modem spaces and are thought to be helpful in understanding spaces where ramps are used.

• Land and Housing Review
• /
• v.11 no.2
• /
• pp.47-57
• /
• 2020

In this study, we aimed to identify the latest trends of landscape in apartment complexes by identifying how landscaping spaces are being created and what their characteristics are. Furthermore, we aimed to find out what type of garden is being constructed in the landscaping space and what the difference between the landscaping space and the garden space is, and to define the future direction of landscape for apartment complexes. The following results were our findings. First, we identified that landscaping space is divided into general landscaping space and garden space. The garden space has designated area within the whole apartment complex as a garden and there is a variety of garden themes and plants, facilities, packaging patterns, and sculptures are used accordingly. On the other hands general landscaping space features uniform patterns of packaging and simple planting patterns. Our finding is that the current trend is to set up separate garden space within the landscaping space of apartment complexes. Although gardens are often regarded as personal property and spaces that need to be cultivated or managed, and spaces that are limited to fences are defined as gardens, the current landscaping space of apartments is creating gardens-like spaces within public spaces.

• Communications of the Korean Mathematical Society
• /
• v.26 no.3
• /
• pp.483-498
• /
• 2011

In this paper, we introduce a new class of uniformly point-wise R-subweakly commuting self-mappings and prove several common fixed point theorems and best approximation results for uniformly point-wise R-subweakly commuting asymptotically I-nonexpansive mappings in normed linear spaces. We also establish some results concerning strong convergence of nearest common fixed points of asymptotically I-non-expansive mappings in reflexive Banach spaces with a uniformly G$\^{a}$teaux differentiable norm. Our results unify and generalize various known results given by some authors to a more general class of noncommuting mappings.

• Journal of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.171-194
• /
• 2020

For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.

• The Pure and Applied Mathematics
• /
• v.9 no.1
• /
• pp.39-45
• /
• 2002

In this paper, we study the space of almost continuous functions with the topology of uniform convergence. And we investigate some properties of this space.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.505-511
• /
• 2015

In this paper, we investigate relationships among property ($k-{\beta}$), weak property (${\beta}_k$), k-nearly uniformly convexity and property ($A_k$).

• Korean Journal of Mathematics
• /
• v.22 no.3
• /
• pp.463-469
• /
• 2014

In this paper, we investigate relationship between superreflexivity and weak property (${\beta}_k$). Indeed, we get the following diagram.