• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.479-499
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• 2014

In this paper, we propose new iteration methods for finding a common point of the solution set of a pseudomonotone equilibrium problem and the solution set of a monotone equilibrium problem. The methods are based on both the extragradient-type method and the viscosity approximation method. We obtain weak convergence theorems for the sequences generated by these methods in a real Hilbert space.

• Journal of the Korean Society of Industry Convergence
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• v.6 no.1
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• pp.23-29
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• 2003

This paper proposes an efficient feature extraction of the images by using independent component analysis(ICA) based on neural networks of the hybrid learning algorithm. The proposed learning algorithm is the fixed point(FP) algorithm based on Newton method and moment. The Newton method, which uses to the tangent line for estimating the root of function, is applied for fast updating the inverse mixing matrix. The moment is also applied for getting the better speed-up by restraining an oscillation due to compute the tangent line. The proposed algorithm has been applied to the 10,000 image patches of $12{\times}12$-pixel that are extracted from 13 natural images. The 144 features of $12{\times}12$-pixel and the 160 features of $16{\times}16$-pixel have been extracted from all patches, respectively. The simulation results show that the extracted features have a localized characteristics being included in the images in space, as well as in frequency and orientation. And the proposed algorithm has better performances of the learning speed than those using the conventional FP algorithm based on Newton method.

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.777-798
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• 2018

In this paper, we study a new iterative method for solving mixed equilibrium problem and a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. Moreover, we prove a strong convergence theorem for finding common fixed points which also are solutions of a mixed equilibrium problem.

• Journal of the Korea Society of Computer and Information
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• v.25 no.3
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• pp.169-176
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• 2020

This study suggested a method to increase the quality of chest compressions in patients with cardiac arrest during transport. When providing cardiopulmonary resuscitation to a cardiac arrest patient in the pre-hospital phase, the quality of chest compressions should be improved by using a three-point fixed belt to the ambulance. Because the quality of the chest compression was increased when the 119 paramedic wears a 3-point fixed belt in addition to the chest compression method. Also, paramedics are less likely to be at risk. Therefore, if a 3-point fixed belt is worn in an ambulance during transport, 119 paramedics will be able to secure safety and provide high-quality chest compressions to cardiac arrest patients.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.91-102
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• 2021

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1529-1540
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• 2018

The matrix equation $X^p+A^*XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix p-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.

• Journal of the Korean Society of Industry Convergence
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• v.8 no.3
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• pp.143-148
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• 2005

This paper presents a hybrid method for recognizing the faces by using principal component analysis(PCA) and fixed-point independent component analysis(FP-ICA). PCA is used to whiten the data, which reduces the effects of second-order statistics to the nonlinearities. FP-ICA is applied to extract the statistically independent features of face image. The proposed method has been applied to the problems for recognizing the 20 face images(10 persons * 2 scenes) of 324*243 pixels from Yale face database. The 3 distances such as city-block, Euclidean, negative angle are used as measures when match the probe images to the nearest gallery images. The experimental results show that the proposed method has a superior recognition performances(speed, rate). The negative angle has been relatively achieved more an accurate similarity than city-block or Euclidean.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.421-436
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• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.135-173
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• 2023

The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.781-802
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• 2024

In this paper, we propose an inertial method for solving a common solution to fixed point and Variational Inequality Problem in Hilbert spaces. Under some standard and suitable assumptions on the control parameters, we prove that the sequence generated by the proposed algorithm converges strongly to an element in the solution set of Variational Inequality Problem associated with a quasimonotone operator which is also solution to a fixed point problem for a demimetric mapping. Finally, we give some numerical experiments for supporting our main results and also compare with some earlier announced methods in the literature.