• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.991-1002
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• 2011

An iterative algorithm is provided to find a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of some variational inequality in a Hilbert space. Using this result, we consider a strong convergence result for finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping. Our results include the previous results as special cases and can be viewed as an improvement and refinement of the previously known results.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.361-369
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• 2012

We get a theorem which shows the existence of at least six solutions for the semilinear wave equation with nonlinearity crossing three eigenvalues. We obtain this result by the variational reduction method and the geometric mapping defined on the finite dimensional subspace. We use a contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three-dimensional subspace with three axes spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one-dimensional subspace.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.507-515
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• 2012

We investigate the number of the solutions for the elliptic boundary value problem. We obtain a theorem which shows the existence of six weak solutions for the elliptic problem with jumping nonlinearity crossing three eigenvalues. We get this result by using the geometric mapping defined on the finite dimensional subspace. We use the contraction mapping principle to reduce the problem on the infinite dimensional space to that on the finite dimensional subspace. We construct a three dimensional subspace with three axis spanned by three eigenvalues and a mapping from the finite dimensional subspace to the one dimensional subspace.

• Communications of the Korean Mathematical Society
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• v.18 no.2
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• pp.251-261
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• 2003

The purpose of this paper is to establish the necessary and sufficient conditions which ensure the strong convergence of the Ishikawa iterative schemes with errors to the unique fixed point of a $\Phi$-hemicontractive mapping defined on a nonempty convex subset of a normed linear space. The results of this paper extend substantially most of the recent results.

• Progress in Superconductivity and Cryogenics
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• v.18 no.2
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• pp.30-36
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• 2016

For the magnetic field analysis or design, it is important to know the behavior of the magnetic field in an interesting space. Magnetic field mapping becomes a useful tool for the study of magnetic field. In this paper, a numerical way for mapping the magnetic field within the cylindrical center volume of magnet is presented, based on the solution of the Laplace's equation in the cylindrical coordinate system. The expression of the magnetic field can be obtained by the magnetic flux density, which measured in the mapped volume. According to the form of the expression, the measurement points are arranged with the parallel cylindrical line (PCL) method. As example, the magnetic flux density generated by an electron cyclotron resonance ion source (ECRIS) magnet and a quadrupole magnet were mapped using the PCL method, respectively. The mapping results show the PCL arrangement method is feasible and convenience to map the magnetic field within a cylindrical center volume generated by the general magnet.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.5
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• pp.695-698
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• 2009

In this paper, we introduce the concept of fuzzy r-generalized open sets which are generalizations of fuzzy r-open sets defined by Lee and Lee [2] and obtain some basic properties of their structures. Also we introduce and study the concepts of fuzzy r-generalized continuous mapping, fuzzy r-generalized open mapping and fuzzy r-generalized closed mapping.

• Journal of Astronomy and Space Sciences
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• v.27 no.3
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• pp.221-230
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• 2010

A 4+12+16 amplitude phase shift keying (APSK) modulation outperforms other 32-APSK modulations in a nonlinear additive white Gaussian noise (AWGN) channel because of its intrinsic robustness against AM/AM and AM/PM distortions caused by the nonlinear characteristics of a high-power amplifier. Thus, this modulation scheme has been adopted in the digital video broadcasting-satellite2 European standard. And it has been considered for high rate transmission of telemetry data on deep space communications in consultative committee for space data systems which provides a forum for discussion of common problems in the development and operation of space data systems. In this paper, we present an improved bits-to-symbol mapping scheme with a better bit error rate for a 4+12+16 APSK signal in a nonlinear AWGN channel and propose a simple signal detection algorithm for the 4+12+16 APSK from the presented bit mapping.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.881-893
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• 2015

In this paper, we introduce the weakly monotone $Pre{\check{s}}i{\acute{c}}$ type mappings in product spaces when the underlying space is an ordered cone metric space. Some fixed point results for such mappings are also proved which generalize and unify several known results in metric and cone metric spaces with normal cone. The results are supported by examples.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.81-87
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• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.667-674
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• 2009

In this paper, a new one-step iterative scheme with error for approximating common fixed points of asymptotically quasi-nonexpansive type nonself-mappings in Banach space is defined. The results obtained in this paper extend and improve the recent ones, announced by H. Y. Zhou, Y. J. Cho, and S. M. Kang [Zhou et al.,(2007), namely, A new iterative algorithm for approximating common fixed points for asymptotically non-expansive mappings, published to Fixed Point Theory and Applications 2007 : 1-9], and many others.