• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.407-418
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• 1997

In this paper we establish the equivalence between the general resolvent equations and variational inequalities. This equiva-lence is used to suggest and analyze a number of iterative algorithms for solving variational inclusions. We also study the convergence criteria of the iterative algorithms. Our results include several pre-viously known results as special cases.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.67-80
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• 2002

We formulate a pair of nondifferentiable symmetric dual variational problems with a square root term. Under invexity assumptions, we establish weak, strong, converse and self duality theorems for our variational problems by using the generalized Schwarz inequality. Also, we give the static case of our nondifferentiable symmetric duality results.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.331-340
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• 2009

We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

• Communications of the Korean Mathematical Society
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• v.25 no.2
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• pp.207-214
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• 2010

In this paper, a generalized variational inequality problem is considered. An iterative method is studied for approximating a solution of the generalized variational inequality problem. Strong convergence theorem are established in a real Hilbert space.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.327-332
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• 2007

A variational inequality defined by the second-order cone is considered, and it is shown that a necessary and sufficient condition for a solution of the variational inequality holds under some regularity condition.

• The Pure and Applied Mathematics
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• v.13 no.3 s.33
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• pp.197-206
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• 2006

This paper introduces a class of multivalued mixed quasi-variational-like ineqcalities and shows the existence of solutions to the class of quasi-variational-like inequalities in reflexive Banach spaces.

• Journal of Internet Computing and Services
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• v.22 no.2
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• pp.1-9
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• 2021

Traditionally, most malicious codes have been analyzed using feature information extracted by domain experts. However, this feature-based analysis method depends on the analyst's capabilities and has limitations in detecting variant malicious codes that have modified existing malicious codes. In this study, we propose a ResNet-Variational AutoEncder-based variant malware classification method that can classify a family of variant malware without domain expert intervention. The Variational AutoEncoder network has the characteristics of creating new data within a normal distribution and understanding the characteristics of the data well in the learning process of training data provided as input values. In this study, important features of malicious code could be extracted by extracting latent variables in the learning process of Variational AutoEncoder. In addition, transfer learning was performed to better learn the characteristics of the training data and increase the efficiency of learning. The learning parameters of the ResNet-152 model pre-trained with the ImageNet Dataset were transferred to the learning parameters of the Encoder Network. The ResNet-Variational AutoEncoder that performed transfer learning showed higher performance than the existing Variational AutoEncoder and provided learning efficiency. Meanwhile, an ensemble model, Stacking Classifier, was used as a method for classifying variant malicious codes. As a result of learning the Stacking Classifier based on the characteristic data of the variant malware extracted by the Encoder Network of the ResNet-VAE model, an accuracy of 98.66% and an F1-Score of 98.68 were obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.239-247
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.465-472
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• 2010

The purpose of this article is to introduce a new generalized class of the Wiener-Hopf equations and a new generalized class of the variational inequalities. Using the projection technique, we show that the generalized Wiener-Hopf equations are equivalent to the generalized variational inequalities. We use this alternative equivalence to suggest and analyze an iterative scheme for finding the solution of the generalized Wiener-Hopf equations and the solution of the generalized variational inequalities. The results presented in this paper may be viewed as significant and improvement of the previously known results. In special, our results improve and extend the resent results of M.A. Noor and Z.Y.Huang[M.A. Noor and Z.Y.Huang, Wiener-Hopf equation technique for variational inequalities and nonexpansive mappings, Appl. Math. Comput.(2007), doi:10.1016/j.amc.2007.02.117].