• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권3호
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• pp.195-206
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• 2014

In this paper, we consider, under a hybrid iterative scheme with errors, a weak convergence theorem to a common element of the set of a finite family of asymptotically k-strictly pseudo-contractive mappings and a solution set of an equilibrium problem for a given bifunction, which is the approximation version of the corresponding results of Kumam et al.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.101-123
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• 2019

In this paper, we consider a system of nonlinear variational type inclusions involving ($H,{\varphi},{\eta}$)-monotone operators in real Banach spaces. Further, we define a proximal operator associated with an ($H,{\varphi},{\eta}$)-monotone operator and show that it is single valued and Lipschitz continuous. Using proximal point operator techniques, we prove the existence and uniqueness of a solution and suggest an iterative algorithm for the system of nonlinear variational type inclusions. Furthermore, we discuss the convergence of the iterative sequences generated by the algorithms.

• 품질경영학회지
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• 제40권4호
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• pp.481-496
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• 2012

Purpose: This paper aims at improving inefficiency of an existing posterior preference articulation method proposed for dual response surface optimization. The method generates a set of non-dominated solutions and then allows a decision maker (DM) to select the best solution among them through an interval selection strategy. Methods: This paper proposes an iterative posterior preference articulation method, which repeatedly generates the predetermined number of non-dominated solutions in an interval which becomes gradually narrower over rounds. Results: The existing method generates a good number of non-dominated solutions not used in the DM's selection process, while the proposed method generates the minimal number of non-dominated solutions necessitated in the selection process. Conclusion: The proposed method enables a satisfactory compromise solution to be achieved with minimal cognitive burden of the DM as well as with light computation load in generating non-dominated solutions.

• 대한수학회보
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• 제47권2호
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• pp.263-274
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• 2010

In this paper, a new class of general nonlinear variational inclusions involving H-monotone is introduced and studied in Hilbert spaces. By applying the resolvent operator associated with H-monotone, we prove the existence and uniqueness theorems of solution for the general nonlinear variational inclusion, construct an iterative algorithm for computing approximation solution of the general nonlinear variational inclusion and discuss the convergence of the iterative sequence generated by the algorithm. The results presented in this paper improve and extend many known results in recent literatures.

• Structural Engineering and Mechanics
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• 제45권5호
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• pp.613-629
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• 2013

In this article we will present a method to directly evaluate the critical point of a non-linear system by using the solution of a polynomial eigenvalue approximation as a starting point for an iterative non-linear system solver. This method will be used to evaluate out-of-plane buckling properties of truss structures for which the lateral displacement of the upper chord has been prevented. The aim is to assess for a number of example structures whether or not the linearized eigenvalue solution gives a relevant starting point for an iterative non-linear system solver in order to find the minimum positive critical load.

• 대한수학회논문집
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• 제22권2호
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• pp.247-258
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• 2007

In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.

• 한국통신학회논문지
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• 제35권9C호
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• pp.743-747
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• 2010

본 논문은 빠른 연산(수렴)을 위한 적응 반복 하이브리드 영상 복원 알고리즘을 제안한다. 공간 영역의 국부제약 정보 설정을 위해 국부 영역의 분산, 평균, 국부 최대값을 이용하였다. 반복 기법을 이용하여 매 반복 해에서 얻어진 복원 영상으로부터 상기 제약 정보를 설정하고, 국부 완화도 결정을 위해 사용된다. 제안된 방식은 일반적인 RCLS(Regularized Constrained Least Squares) 방식에 비해 빠른 수렴속도와 더 좋은 성능을 얻을 수 있다.

• 대한수학회지
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• 제58권3호
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• pp.525-552
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• 2021

In this paper, we introduce two general iterative algorithms (one implicit algorithm and one explicit algorithm) for finding a common element of the solution set of the variational inequality problems for a continuous monotone mapping, the zero point set of a set-valued maximal monotone operator, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative algorithms to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.717-731
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• 2021

In this paper, we introduce and study a new class of random generalized nonlinear implicit variational-like inclusion with random fuzzy mappings in a real separable Hilbert space and give its fixed point formulation. Using the fixed point formulation and the proximal mapping technique for strongly maximal monotone mapping, we suggest and analyze a random iterative scheme for finding the approximate solution of this class of inclusion. Further, we prove the existence of solution and discuss the convergence analysis of iterative scheme of this class of inclusion. Our results in this paper improve and generalize several known results in the literature.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.179-195
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• 2024

In this article, we study the Picard-Ishikawa iterative method for approximating the fixed point of generalized α-Reich-Suzuki nonexpanisive mappings. The weak and strong convergence theorems of the considered method are established with mild assumptions. Numerical example is provided to illustrate the computational efficiency of the studied method. We apply our results to the solution of a nonlinear delay integral equation. The results in this article are improvements of well-known results.