• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.2
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• pp.471-485
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• 2023

As data sharing increases explosively, such information encoded in QR code is completely public as private messages are not securely protected. This paper proposes a new 'PROMISE' framework for hiding information based on the QR code projection matrix by using image segmentation without modifying the essential QR code characteristics. Projection matrix mapping, matrix scrambling, fusion image segmentation and steganography with SEL(secret embedding logic) are part of the PROMISE framework. The QR code could be mapped to determine the segmentation site of the fusion image as a binary information matrix. To further protect the site information, matrix scrambling could be adopted after the mapping phase. Image segmentation is then performed on the fusion image and the SEL module is applied to embed the secret message into the fusion image. Matrix transformation and SEL parameters should be uploaded to the server as the secret key for authorized users to decode the private message. And it was possible to further obtain the private message hidden by the framework we proposed. Experimental findings show that when compared to some traditional information hiding methods, better anti-detection performance, greater secret key space and lower complexity could be obtained in our work.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.447-456
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• 2017

The purpose of this paper is to introduce some strong convergence theorems for the problem of finding a common zero of a finite family of monotone operators and the problem of finding a common fixed point of a finite family of nonexpansive in Hilbert spaces by hybrid projection method.

• Communications of the Korean Mathematical Society
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• v.28 no.1
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• pp.191-207
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• 2013

In this paper, we introduce the shrinking projection method for hemi-relatively nonexpansive mappings to find a common solution of variational inequality problems and equilibrium problems in uniformly convex and uniformly smooth Banach spaces and prove some strong convergence theorems to the common solution by using the proposed method.

• East Asian mathematical journal
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• v.28 no.3
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• pp.305-320
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• 2012

The purpose of this paper is to introduce a hybrid projection method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a variational inclusion problem and the set of common fixed points of a finite family of strict pseudo-contractions in Hilbert spaces.

• Korean Journal of Mathematics
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• v.18 no.2
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• pp.105-118
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• 2010

The purpose of this paper is to consider an iterative method for an equilibrium problem and a family relatively nonexpansive mappings. Weak convergence theorems are established in uniformly smooth and uniformly convex Banach spaces.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.16 no.2
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• pp.299-309
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• 1998

The national coordinate system is an essential component for a geographic/land information system, since it provides the spatial reference for expressing position information. The national mapping of Korea has been based on 3-different meridians on the Gauss-Schreiber projection in year 1910s, later this was changed to the Gauss-Kruger projection. Existing map coordinate systems maintaining the national land survey project on 1910s, have some structural shortcomings of unknown computational procedures and projection methods. In this paper, the problems of the map coordinates usage and of longitudes origin shift(10.405") and their solutions are investigated. Also, this study discusses the issues involved in choosing coordinate system for digital mapping and their applications as a basis for spatial data management. The foreign country's coordinate systems are reviewed and the elements to realize a new unified grid coordinate system is proposed. The Transverse Mercator projection with a central meridian of $127^\circ\;30'$, scale factor 0.9996, and GRS80 ellipsoid, is selected in Korean peninsula.sula.

• East Asian mathematical journal
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• v.27 no.1
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• pp.1-9
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• 2011

In this paper, we consider an iterative scheme for finding a common element of the set of fixed points of a asymptotically quasi nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using this result, we consider the problem of finding a common fixed point of a asymptotically quasi-nonexpansive mapping and strictly pseudocontractive mapping and the problem of finding a common element of the set of fixed points of a asymptotically quasi-nonexpansive mapping and the set of zeros of an inverse-strongly monotone mapping.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.293-309
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• 2011

The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article apply above results to prove the strong convergence theorems of zero point for maximal monotone operators in Banach spaces. Noting that, the CQ iteration method can be used for relatively nonexpansive mapping but it can not be used for weak relatively nonexpansive mapping. However, the monotone CQ method can be used for weak relatively nonexpansive mapping. The results of this paper modify and improve the results of S.Matsushita and W.Takahashi, and some others.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.181-198
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• 2016

In this work, we suggest a new system of generalized nonlinear regularized nonconvex variational inequalities in a real Hilbert space and establish an equivalence relation between this system and fixed point problems. By using the equivalence relation we suggest a new perturbed projection iterative algorithms with mixed errors for finding a solution set of system of generalized nonlinear regularized nonconvex variational inequalities.