• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.81-89
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• 2007

In this paper, we introduce the concept of a system of asymptotically quasinonexpansive type mappings. Furthermore, we define a $k$-step iterative sequence approximating common fixed point for a system of asymptotically quasi-nonexpansive type mappings and study its stability in real Banach spaces.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1323-1339
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• 2008

In this paper, a new class of $(h,{\eta})$-proximal for proper functionals in Hilbert spaces is introduced. The existence and Lip-schitz continuity of the $(h,{\eta})$-proximal mappings for proper functionals are proved. A class of generalized nonlinear quasi-variational-like inclusions in Hilbert spaces is introduced. A perturbed three-step iterative algorithm with errors for the generalized nonlinear quasi-variational-like inclusion is suggested. The existence and uniqueness theorems of solution for the generalized nonlinear quasi-variational-like inclusion are established. The convergence and stability results of iterative sequence generated by the perturbed three-step iterative algorithm with errors are discussed.

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.201-209
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• 2006

Suppose C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T : $C{\rightarrow}C$ be an asymptotically nonexpansive in the intermediate sense mapping. In this paper we introduced the three-step iterative sequence for such map with error members. Moreover, we prove that, if T is completely continuous then the our iterative sequence converges strongly to a fixed point of T.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.557-566
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• 2009

In this paper, we present the three-step mean value iterative scheme and prove that the iteration sequence converge strongly to a common element of the set of fixed points of a nonexpansive mappings and the set of the solutions of the variational inclusions under some mild conditions. The results presented in this paper extend, generalize and improve the results of Noor and Huang and some others.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.83-95
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• 2014

In a uniformly convex Banach space, we introduce a iterative scheme for a finite family of asymptotically quasi-nonexpansive mappings and utilize a new inequality to prove several convergence results for the iterative sequence. The results generalize and unify many important known results of relevant scholars.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.401-415
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• 2015

In this paper, we propose a modified proximal point algorithm which consists of a resolvent operator technique step followed by a generalized projection onto a moving half-space for approximating a solution of a variational inclusion involving a maximal monotone mapping and a monotone, bounded and continuous operator in Banach spaces. The weak convergence of the iterative sequence generated by the algorithm is also proved.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.49 no.3
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• pp.111-116
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• 2000

In this paper, we presented a new algebraic iterative algorithm for the optimal control of the nonlinear systems. The algorithm is based on tow steps. The first step transforms optimal control problem into a sequence of linear optimal control problem using the quasilinearization method. In the second step, TPB(two point boundary condition problem) is solved by algebraic equations instead of differential equations using BPF(block pulse functions). The proposed algorithm is simple and efficient in computation for the optimal control of nonlinear systems. In computer simulation, the algorithm was verified through the optimal control design of Van del pole system and Volterra Predatory-prey system.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.673-676
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• 2003

This paper deals with the problem of moving object detection and location in computer vision. We describe a new object-dependent motion analysis method for tracking target in an image sequence taken from a moving platform. We tackle these tasks with three steps. First, we make an active contour model of a target in order to build some of low-energy points, which are called kernels. Then we detect interest points in two windows called tracking windows around a kernel respectively. At the third step, we decide the correspondence of those detected interest points between tracking windows by the probabilistic relaxation method In this algorithm, the detecting process is iterative and begins with the detection of all potential correspondence pair in consecutive image. Each pair of corresponding points is then iteratively recomputed to get a globally optimum set of pairwise correspondences.

• Journal of Mechanical Science and Technology
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• v.15 no.1
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• pp.125-138
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• 2001

An efficient correction storage scheme on a structured grid is applied to a sequence of approximate Jacobian systems arising at each time step from a linearization of the discrete nonlenear system of equations, obtained by the implicit time discretization of the conservation laws for unsteady fluid flows. The contribution of freezing the Jacobian matrix to computing costs is investigated within the correction storage scheme. The performance of the procedure is exhibited by measuring CPU time required to obtain a fully developed laminar vortex shedding flow past a circular cylinder, and is compared with that of a collective iterative method on a single grid. In addition, some computed results of the flow are presented in terms of some functionals along with measured data. The computational test shows that the computing costs may be saved in favor of the correction storage scheme with the frozen Jacobian matrix, to a great extent.