• East Asian mathematical journal
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• v.18 no.2
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• pp.211-218
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• 2002

In this paper, we introduce the notion of almost topological convergence spaces and almost pretopological convergence spaces, and prove that these are product invariant.

• East Asian mathematical journal
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• v.17 no.2
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• pp.217-224
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• 2001

In this paper, we introduce the notion of some modification of given convergence structure and product convergence. Also, we find some properties which hold between the modification associated with a product of convergence structures and the product of modifications associated with the factor convergence structures.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.265-286
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• 2023

In this paper, we introduce and study a generalized Cayley operator associated to H(·, ·)-monotone operator in semi-inner product spaces. Using the notion of graph convergence, we give the equivalence result between graph convergence and convergence of generalized Cayley operator for the H(·, ·)-monotone operator without using the convergence of the associated resolvent operator. To support our claim, we construct a numerical example. As an application, we consider a system of generalized Cayley inclusions involving H(·, ·)-monotone operators and give the existence and uniqueness of the solution for this system. Finally, we propose a perturbed iterative algorithm for finding the approximate solution and discuss the convergence of iterative sequences generated by the perturbed iterative algorithm.

• East Asian mathematical journal
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• v.24 no.1
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• pp.27-33
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• 2008

The purpose of this paper is to establish the weak convergence theorem of Mann iterative sequence for nonexpansive mappings in probabilistic Hilbert spaces. In order to establish the weak convergence theorem, a new method was presented in this paper, that is method of mathematical expectation.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1579-1586
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• 2015

In this paper we investigate the barrellednes of some spaces of X-valued measures, X being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space X into a barrelled normed space Y, equipped with the uniform convergence topology.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.901-911
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• 2023

In this paper a generalization of convergent sequences in connection with generalized topologies and filters is given. Additionally, properties such as uniqueness, behavior related to continuous functions are established and notions relative to product spaces.

• Journal of the Korean Mathematical Society
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• v.50 no.6
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• pp.1291-1310
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• 2013

This paper develops least-squares pseudo-spectral collocation methods for elliptic boundary value problems having interface conditions given by discontinuous coefficients and singular source term. From the discontinuities of coefficients and singular source term, we derive the interface conditions and then we impose such interface conditions to solution spaces. We define two types of discrete least-squares functionals summing discontinuous spectral norms of the residual equations over two sub-domains. In this paper, we show that the homogeneous least-squares functionals are equivalent to appropriate product norms and the proposed methods have the spectral convergence. Finally, we present some numerical results to provide evidences for analysis and spectral convergence of the proposed methods.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.927-944
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• 2022

Let $\vec{p}{\in}(0,\;1]^n$ be an n-dimensional vector and A a dilation. Let $H^{\vec{p}}_A(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H^{\vec{p}}_A(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f{\in}H^{\vec{p}}_A(\mathbb{R}^n)$ coincides with a continuous function F on ℝⁿ in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H^{\vec{p}}_A(\mathbb{R}^n)$.

• Fashion & Textile Research Journal
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• v.21 no.2
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• pp.133-140
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• 2019

This study developed smart fashion prototypes that provide utilitarian functionality by combining Fashion and Electronics regarding the IT focused convergence tendency in modern industries. A convergence R&D workshop was performed by Fashion design majors and Engineering majors for the study. As a result, 5 functional smart fashion prototypes were developed and the outline of each prototype are as follows. The $1^{st}$ prototype, 'Hidden Camera Detecting Coat' focused on gender-related crimes. The coat uses infrared lighting and LED technologies to provide a function to detect hidden cameras in suspicious public spaces such as toilets. The $2^{nd}$ prototype, 'Heating-massage Suit' targeted patients with musculoskeletal system difficulties. The suit uses heating and vibration technologies to provide a heating massage treatment for patients with ongoing difficulties in their daily lives. The $3^{rd}$ prototype is an air-bag jacket to prevent sexual molestation on public transportation. The jacket extends its volume through pressure sensing, air compressing, motors and 3D-printing technology to secure the wearer's personal preventive space between the user's body and others. The $4^{th}$ prototype is a town wear for people suffering from synesthesia. People with synesthesia inadvertently see colors when exposed to certain sounds. This town wear uses sound sensing, air compressing, motors and 3D-printing technology to provide sound prevention and a comfortable sound playing function. The $5^{th}$ prototype is a set of a vest and a gloves for visually impaired people. The vest and gloves uses DMS, voice playing, vibration technology to provide distance measuring and warning functions.