• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.565-575
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• 2013

Let H be a real Hilbert space and let T : H ${\rightarrow}$ H be a Lipschitz pseudocontractive mapping. We introduce a modified Ishikawa iterative algorithm and prove that if $F(T)=\{x{\in}H:Tx=x\}{\neq}{\emptyset}$, then our proposed iterative algorithm converges strongly to a fixed point of T. No compactness assumption is imposed on T and no further requirement is imposed on F(T).

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.693-702
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• 2009

In this paper, we introduce and study a system of mixed variational inequalities in Banach spaces. By using J-proximal mapping and its Lipschitz continuity for a nonconvex, lower semicontinuous, subdifferentiable, proper functional, an iterative algorithm for computing the approximate solutions of system of mixed variational inequalities is suggested and analyzed. The convergence criteria of the iterative sequences generated by iterative algorithm is also discussed.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.13-31
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• 2015

In this paper, we introduce a general iterative algorithm for finding a common element of the common fixed point set of an infinite family of ${\lambda}_i$-strict pseudo-contractions and the solution set of a general system of variational inclusions for two inverse strongly accretive operators in q-uniformly smooth Banach spaces. Then, we analyze the strong convergence of the iterative sequence generated by the proposed iterative algorithm under mild conditions.

• Korean Journal of Optics and Photonics
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• v.9 no.6
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• pp.390-395
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• 1998

Iterative Fourier transform algorithm (IFTA) was utilized for the phase retrieval problem or the optimal of the IFTA depends strongly on the selection of initial phase value. In this paper, we proposed the modified interactive Fourier transform algorithm in order to improve the convergence speed of error and the stability of convergence. The modified IFTA was reduced number of iteration about 30% than existing IFTA with the image size of 128$\times$128 pixel.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.61-70
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• 2020

In this paper, we introduce a new concept of stability of coincidence iterative algorithm for three mappings and derive a new three-step Jungck-type iterative algorithm. And, we prove a stability result and a strong convergence result for the Jungck-type algorithm using the M_J-contractive condition. Our results extend and unify the corresponding ones in [3, 6, 7, 13].

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.40 no.5
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• pp.298-311
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• 2003

Iterative Fourier transform algorithm, (IFTA) is tile iterative numerical algorithm for the design of the diffractive optical elements (DOE), by which the phase distribution of a DOE converges on a local optimal solution. The convergence of IFTA depends on several factors 3s initial phase distribution, the structure of the degree of freedom on the observation plane, and the values of internal parameters. In this paper, we analyze tile dependence of the convergence of IFTA on an internal parameter of IFTA, the relaxation parameter, and propose a new hybrid scheme of genetic algorithm and IFTA to obtain more accurate solution.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.1031-1047
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• 2017

In this paper, we introduce two general iterative algorithms (one implicit algorithm and other explicit algorithm) for nonexpansive mappings in a reflexive Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm. Strong convergence theorems for the sequences generated by the proposed algorithms are established.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.909-920
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• 2011

A regularized Newton method for nonlinear ill-posed problems is considered. In each Newton step an implicit iterative method with an appropriate stopping rule is proposed and analyzed. Under certain assumptions on the nonlinear operator, the convergence of the algorithm is proved and the algorithm is stable if the discrepancy principle is used to terminate the outer iteration. Numerical experiment shows the effectiveness of the method.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.237-251
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• 2006

In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.346-346
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• 2000

We proposed a method of second-order iterative learning control with feedback, which shows an enhancement of convergence speed and robustness to the disturbances in our previous study. In this paper, we show that the proposed second-order iterative learning control algorithm with feedback is more effective and has better convergence performance than the algorithm without feedback in the case of the existence of initial condition errors. And the convergence woof of the proposed algorithm in the case of the existence of initial condition error is given in detail, and the effectiveness of the Proposed algorithm is shown by simulation results.