• 대한수학회논문집
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• 제25권2호
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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.

• 한국경영과학회지
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• 제9권2호
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• pp.28-33
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• 1984

In this paper some procedures are given whereby an analytic solution may be found for the Riccati differential equation and algebraic Riccati equation in optimal control theory. Some iterative techniques for solving these equations are presented. Rate of convergence and initialization of the iterative processes are discussed.

• Structural Engineering and Mechanics
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• 제83권3호
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• pp.353-361
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• 2022

Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.

• 대한수학회논문집
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• 제20권1호
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• pp.71-78
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• 2005

In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$-strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].

• Korean Journal of Mathematics
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• 제4권2호
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• pp.83-88
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• 1996

In 1994 Z.Liang constructed an iterative method for the solution of nonlinear equations involving m-accretive operators in uniformly smooth Banach spaces. In this paper we apply the slight variants of Liang's iterative methods and generalize the results of Z.Liang. Moreover our proof is more simple than Liang's proof.

• 대한수학회논문집
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• 제9권4호
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• pp.819-823
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• 1994

If H is a Hilbert space, then an operator $T : D(T) \subset H \to H$ is said to be monotone if $$ (x-y, Tx-Ty) \geq 0$$ for any x, y in D(T). Many authors [1], [4] obtained the existence theorem for the equation $y = x + Tx$ for x, given an element y in H and a monotone operator T. On the other hand some iterative methods were applied to the approximations for the solution of the above equation [6], [8]. For example Bruck [2] obtained the iterative solution of the above equation with an explicit error estimate as follows.

• 산업경영시스템학회지
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• 제22권50호
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• pp.333-340
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• 1999

An ideal traffic control system should consider simultaneously both route guidance of vehicles and signal policies at intersection of a traffic network. It is known that an iterative procedure gives an optimal route to each vehicle in the network. This paper presents an iterative procedure to find an optimal signal plan for the network. We define the optimal solution as a signal equilibrium. From the definition of signal equilibrium, we prove that the fixed point solution of the iterative procedure is a signal equilibrium, when optimal signal algorithms are implemented at each intersection of the network. A combined model of route guidance and signal planning is also suggested by relating the route guidance procedure and the signal planning procedure into a single loop iterative procedure.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.749-780
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• 2021

In this paper, we give the notion of M(., .)-𝜂-proximal mapping for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. As an application, we introduce and investigate a new system of variational-like inclusions in Banach spaces. By means of M(., .)-𝜂-proximal mapping method, we give the existence of solution for the system of variational inclusions. Further, propose an iterative algorithm for finding the approximate solution of this class of variational inclusions. Furthermore, we discuss the convergence and stability analysis of the iterative algorithm. The results presented in this paper may be further expolited to solve some more important classes of problems in this direction.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.471-497
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• 2022

In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.265-286
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• 2023

In this paper, we introduce and study a generalized Cayley operator associated to H(·, ·)-monotone operator in semi-inner product spaces. Using the notion of graph convergence, we give the equivalence result between graph convergence and convergence of generalized Cayley operator for the H(·, ·)-monotone operator without using the convergence of the associated resolvent operator. To support our claim, we construct a numerical example. As an application, we consider a system of generalized Cayley inclusions involving H(·, ·)-monotone operators and give the existence and uniqueness of the solution for this system. Finally, we propose a perturbed iterative algorithm for finding the approximate solution and discuss the convergence of iterative sequences generated by the perturbed iterative algorithm.