• Communications of the Korean Mathematical Society
• /
• v.33 no.2
• /
• pp.515-525
• /
• 2018

In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.

• International Journal of Contents
• /
• v.3 no.4
• /
• pp.26-29
• /
• 2007

The paper is devoted to problem of spline approximation. A new method of nodes location for curves and surfaces computer construction in multidimensional spaces by means of B-splines is presented. The criteria are which links a square-mean error caused by high frequency spline distortions and approximation intervals is determined and necessary theorem is proved. In this method use a theory of entire multidimensional spectra and may be extended for the spaces of three, four and more variables. Future work: application area such as digital contents like animation, game graphic.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.311-330
• /
• 2020

This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.

• Proceedings of the KIEE Conference
• /
• 2005.10b
• /
• pp.186-188
• /
• 2005

Hand region detection in images is an important process in many computer vision applications. It is a process that usually starts at a pixel-level, and that involves a pre-process of color space transformation followed by a classification process. A color space transformation is assumed to increase separability between skin classes for hands and non-skin classes for other parts, to increase similarity among different skin tones, and to bring a robust performance under varying illumination conditions, without any sound reasonings. In this work, we examine if the color space transformation does bring those benefits to the problem of hand region detection on a dataset of images with different hand postures, backgrounds, people, and illuminations. Results indicate that best of the color space is the normalized RGB.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.433-448
• /
• 1998

In this study we use inexact Newton-like methods to find solutions of nonlinear operator equations on Banach spaces with a convergence structure. Our technique involves the introduction of a generalized norm as an operator from a linear space into a par-tially ordered Banach space. In this way the metric properties of the examined problem can be analyzed more precisely. Moreover this approach allows us to derive from the same theorem on the one hand semi-local results of kantorovich-type and on the other hand 2global results based on monotonicity considerations. By imposing very general Lipschitz-like conditions on the operators involved on the other hand by choosing our operators appropriately we can find sharper error bounds on the distances involved than before. Furthermore we show that special cases of our results reduce to the corresponding ones already in the literature. Finally our results are used to solve integral equations that cannot be solved with existing methods.

• Journal of applied mathematics & informatics
• /
• v.5 no.2
• /
• pp.507-516
• /
• 1998

In this study we are concerned with the problem of ap-proximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4] [5] [8] These results were not given in affine invariant form and made use of a real quadratic majorizing polynomial. Here we provide our re-sults in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.

• East Asian mathematical journal
• /
• v.33 no.1
• /
• pp.83-102
• /
• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.115-122
• /
• 2004

We characterize the additive operators preserving rank-additivity on symmetry matrix spaces. Let $S_{n}(F)$ be the space of all $n\;\times\;n$ symmetry matrices over a field F with 2, $3\;\in\;F^{*}$, then T is an additive injective operator preserving rank-additivity on $S_{n}(F)$ if and only if there exists an invertible matrix $U\;\in\;M_n(F)$ and an injective field homomorphism $\phi$ of F to itself such that $T(X)\;=\;cUX{\phi}U^{T},\;\forallX\;=\;(x_{ij)\;\in\;S_n(F)$ where $c\;\in;F^{*},\;X^{\phi}\;=\;(\phi(x_{ij}))$. As applications, we determine the additive operators preserving minus-order on $S_{n}(F)$ over the field F.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.257-264
• /
• 1992

Since Alfsen and Effors [1] introduced the notion of an M-ideal, many authors [3,6,9,12] have worked on the problem of finding those Banach spaces X and Y for which K(X,Y), the space of all compact linear operators from X to Y, is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y. The M-ideal property of K(X,Y) in L(X,Y) gives some informations on X,Y and K(X,Y). If K(X) (=K(X,X)) is an M-ideal in L(X) (=L(X,X)), then X has the metric compact approximation property [5] and X is an M-ideal in $X^{**}$ [10]. If X is reflexive and K(X) is an M-ideal in L(X), then K(X)$^{**}$ is isometrically isomorphic to L(X)[5]. A weaker notion is a semi M-ideal. Studies on Banach spaces X and Y for which K(X,Y) is a semi M-ideal in L(X,Y) were done by Lima [9, 10].

• Journal of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.479-491
• /
• 2013

Let M be a smooth real hypersurface in complex space of dimension $n$, $n{\geq}3$, and assume that the Levi-form at $z_0$ on M has at least $(q+1)$-positive eigenvalues, $1{\leq}q{\leq}n-2$. We estimate solutions of the local $\bar{\partial}$-closed extension problem near $z_0$ for $(p,q)$-forms in Sobolev spaces. Using this result, we estimate the local solution of tangential Cauchy-Riemann equation near $z_0$ in Sobolev spaces.