• East Asian mathematical journal
• /
• 제28권3호
• /
• pp.265-280
• /
• 2012

In this paper, we introduce an iterative sequence by using a hybrid generalized $f$-projection algorithm for finding a common element of the set of fixed points of a relatively weak nonexpansive mapping an the set of solutions of a generalized variational inequality in a Banach space. Our results extend and improve the recent ones announced by Y. Liu [Strong convergence theorems for variational inequalities and relatively weak nonexpansive mappings, J. Glob. Optim. 46 (2010), 319-329], J. Fan, X. Liu and J. Li [Iterative schemes for approximating solutions of generalized variational inequalities in Banach spaces, Nonlinear Analysis 70 (2009), 3997-4007], and many others.

• 대한수학회지
• /
• 제53권6호
• /
• pp.1331-1345
• /
• 2016

A K-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator K in Hilbert spaces. K-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a K-g-frame, which is different from a g-frame, is discussed. Several construction methods of K-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of K-g-frames are obtained.

• Korean Journal of Mathematics
• /
• 제30권2호
• /
• pp.205-229
• /
• 2022

The aim of this paper is to obtain some results which belong to fixed point theory such as strong convergence, rate of convergence, stability, and data dependence by using the new Jungck-type iteration method for a mapping defined in complex-valued Banach spaces. In addition, some of these results are supported by nontrivial numerical examples. Finally, it is shown that the sequence obtained from the new iteration method converges to the solution of the functional integral equation in complex-valued Banach spaces. The results obtained in this paper may be interpreted as a generalization and improvement of the previously known results.

• 한국실내디자인학회논문집
• /
• 제23권1호
• /
• pp.61-68
• /
• 2014

Recently, there have been increasing attempts to pursue and express feelings such as sensibilities, emotions, and impressiveness in commercial spaces. One of such methods is to apply 'storytelling' to space designs. Applicability of storytelling to a space suggests that the contents of a space can be expressed through various mediums. Portraying events and situations through a single time continuity of a story is referred to as 'narrative'. The movement of users and sequence of contents are determined by a narrative. It provides different storytelling and a sense of place to each space through various roles, such as wide association, engraving, and image formation. A narrative can lead users to engage in different perceptions and behaviors even in spaces with the same content. Thus, this study is intended to examine the impact of space marketing in line with design narratives, assuming that narratives of commercial space designs will influence the formation of brand identity. The research methods are as follows. First, the definition of narratives in space design was established by examining narrative architectures. Second, design analysis tools for commercial spaces were established from the perspective of narratives through preceding studies. Third, the design narratives of different shops under the same brand were comparatively analyzed through a case study. To carry out a case study, a commercial space of 'O'sulloc' was selected, and its brand identity was studied from the narrative standpoint. The case study involved interior designs of 7 road shops of 'O'sulloc.' Among the 7 road shops, two of them with the biggest difference in design narratives were selected, and an observation survey was done on the users as a second analysis. Through the observation survey, actual design narrative experience was analyzed in 4 steps of introduction, development, turn, and conclusion. The findings are as follows. The design method of each shop varied, and different design elements were emphasized. Among various elements, the ones that reflect the brand identity of 'O'sulloc' the best were logo, product, and shape. During the process of narratives, the characteristics of each shop and user recognition and behavior varied depending on the degree of emphasis on a particular element. It suggests that space design narratives can influence the formation of brand identity. This study provides ideal directions of developing space designs necessary for forming brand identity from the standpoint of Korean traditional culture modernization. Future studies could discuss the economic feasibility of such designs.

• 한국실내디자인학회논문집
• /
• 제34호
• /
• pp.78-85
• /
• 2002

This study aims at alalyzing the circulation process, merchandising system of Mosi(Korean traditional garment material), and accessing the way of interior design of Mosi market. There are three kinds of garment material of Mosi such as Pilmosi, Gootmosi, Taemosi classified by manufacturing process. At Mosi market, these three materials are sold in due sequence. Mosi market needs three space zones such as Mosi market space, inspecting space of Mosi and resting place, and these three spaces have strong interrelationship, so designer should plan not to disterb the moving flow. In the Mosi market space there should be divided by three zones such as Pilmosi marketing place, Gootmosi marketing place, and Taemosi marketing place in due sequence. The furniture of Mosi market place divided two kinds such as furniture for Pilmosi and that of Gootmosi or Taemosi. The proper form of furniture for Pilmosi is circular arc bar counter and that for Gootmosi or Taemosi is low rectangular table.

• 대한수학회지
• /
• 제51권1호
• /
• pp.137-162
• /
• 2014

In this work we study the local and semilocal convergence of the relaxed Newton's method, that is Newton's method with a relaxation parameter 0 < ${\lambda}$ < 2. We give a Kantorovich-like theorem that can be applied for operators defined between two Banach spaces. In fact, we obtain the recurrent sequence that majorizes the one given by the method and we characterize its convergence by a result that involves the relaxation parameter ${\lambda}$. We use a new technique that allows us on the one hand to generalize and on the other hand to extend the applicability of the result given initially by Kantorovich for ${\lambda}=1$.

• Korean Journal of Mathematics
• /
• 제8권2호
• /
• pp.121-126
• /
• 2000

B.Djafari Rouhani and W.A.Kirk [3] proved the following theorem: Let Xbe a reflexive Banach space and $(x_n)_{n{\geq}0}$ be a nonexpansive (resp., firmly nonexpansive )sequence in X. Then the set of weak ${\omega}$-limit points of the sequence $(\frac{x_n}{n})_{n{\geq}1}$(resp., $(x_{n+1}-x_n)_{n{\geq}0$) always lies on a convex subset of a sphere centered at the origin of radius $d={\lim}_{n{\rightarrow}{\infty}}\frac{{\parallel}x_n{\parallel}}{n}$. In this paper we show that the above theorem for nonexpansive(resp., firmly nonexpansive) sequences holds in a general Banach space(resp., a strictly convex dual $X^*$).

• 호남수학학술지
• /
• 제29권4호
• /
• pp.523-533
• /
• 2007

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

• 대한수학회지
• /
• 제43권3호
• /
• pp.491-506
• /
• 2006

In this paper, we extend the concept of the group ${\varepsilon}(X)$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group ${\varepsilon}(X,\;A)$ of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence $1\;{\to}\;G\;{\to}\;{\varepsilon}(X,\;A)\;{to}\;{\varepsilon}(A)$ where G is a subgroup of ${\varepsilon}(X,\;A)$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $1\;{\to}\;{\varepsilon}(X)\;{\to}\;{\varepsilon}(X{\times}Y,Y)\;{\to}\;{\varepsilon}(Y)\;{\to}\;1$ provided the two sets $[X{\wedge}Y,\;X{\times}Y]$ and [X, Y] are trivial.

• 대한수학회지
• /
• 제52권6호
• /
• pp.1287-1303
• /
• 2015

The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.