• East Asian mathematical journal
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• v.26 no.3
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• pp.429-440
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• 2010

In this paper, we study a new one-step iterative scheme with error for approximating common fixed points of non-self asymptotically nonexpansive in the intermediate sense mappings in uniformly convex Banach spaces. Also we have proved weak and strong convergence theorems for above said scheme. The results obtained in this paper extend and improve the recent ones, announced by Zhou et al. [27] and many others.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.169.3-169
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• 2001

This paper introduces a new approach to analysis of error convergence for a class of iterative learning control systems. First, a nonlinear plant is represented using a Takagi-Sugeno(T-S) fuzzy model. Then each iterative learning controller is designed for each linear plant in the T-S fuzzy model. From the view point of two-dimensional(2-D) system theory, we transform the proposed learning systems to a 2-D error equation, which is also established in the form of T-S fuzzy model. We analysis the error convergence in the sense of induced 2 L -norm, where the effects of disturbances and initial conditions on 2-D error are considered. The iterative learning controller design problem to guarantee the error convergence can be reduced to linear matrix inequality problems. In comparison with others, our learning algorithm ...

• Coupled systems mechanics
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• v.7 no.6
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• pp.755-774
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• 2018

The Ritz method is known as very successful strategy for discretizing continuous problems, but it has never been used for solving systems of algebraic equations. The Iterated Ritz Method (IRM) is a novel iterative solver based on the discretized Ritz procedure applied at each iteration step. With an appropriate choice of coordinate vectors, the method may be efficient in linear, nonlinear and optimization problems. Additionally, some iterative methods can be explained as special cases of this approach, which helps to understand advantages and limitations of these methods and gives motivation for their improvement in sense of IRM. In this paper, some ideas for generation of efficient coordinate vectors are presented. The algorithm was developed and tested independently and then implemented into the open source program FEAP. Method has been successfully applied to displacement based (even ill-conditioned) models of structural engineering practice. With this original approach, a new iterative solution strategy has been opened.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.5
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• pp.385-392
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• 2002

This paper introduces a new approach to analysis of error convergence for a class of iterative teaming control systems. Firstly, a nonlinear plant is represented using a Takagi-Sugeno(T-S) fuzzy model. Then each iterative learning controller is designed for each linear plant in the T-S fuzzy model. From the view point of two-dimensional(2-D) system theory, we transform the proposed learning systems to a 2-D error equation, which is also established if the form of T-S fuzzy model. We analyze the error convergence in the sense of induced L$_2$-norm, where the effects of disturbances and initial conditions on 2-D error are considered. The iterative teaming controller design problem to guarantee the error convergence can be reduced to the linear matrix inequality problem. This method provides a systematic design procedure for iterative teaming controller. A simulation example is given to illustrate the validity of the proposed method.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.269-277
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• 2008

This paper proposes a necessary and sufficient condition of convergence in the $L_2$-norm sense for a feedback-based iterative learning control (ILC) system including a multi-input multi-output (MIMO) linear time-invariant (LTI) plant. It is shown that the convergence conditions for a nominal plant and an uncertain plant are equal to the nominal performance condition and the robust performance condition in the feedback control theory, respectively. Moreover, no additional effort is required to design an iterative learning controller because the performance weighting matrix is used as an iterative learning controller. By proving that the least upper bound of the $L_2$-norm of the remaining tracking error is less than that of the initial tracking error, this paper shows that the iterative learning controller combined with the feedback controller is more effective to reduce the tracking error than only the feedback controller. The validity of the proposed method is verified through computer simulations.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.621-633
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• 2014

In this paper, we introduce a general iterative algorithm for asymptotically quasi-${\phi}$-nonexpansive mappings in the intermediate sense to have the strong convergence in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

• Journal of Electrical Engineering and information Science
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• v.1 no.2
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• pp.67-76
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• 1996

In the present paper we propose two new improved iterative restoration algorithms. One is to accelerate convergence of the steepest descent method using the improved search directions, while the other accelerates convergence by using preconditioners. It is also shown that the proposed preconditioned algorithm can accelerate iteration-adaptive iterative image restoration algorithm. The preconditioner in the proposed algorithm can be implemented by using the FIR filter structure, so it can be applied to practical application with manageable amount of computation. Experimental results of the proposed methods show good perfomance improvement in the sense of both convergence speed and quality of the restored image. Although the proposed methods cannot be directly included in spatially-adaptive restoration, they can be used as pre-processing for iteration-adaptive algorithms.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.47 no.5
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• pp.145-152
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• 2010

This paper presents a digital auto-focusing algorithm using iterative unsharp mask filter. The proposed digital auto-focusing algorithm has the advantage of low computational complexity because it uses a simple filter instead of calculating the point spread function for the estimation of image degradation. The proposed iterative algorithm can control the number of iterations for image restoration according to the objective and the subjective criterion. We show that the proposed algorithm is mathematically equivalent to the conventional image restoration. Finally, in order to evaluate the performance of the proposed algorithm, various experiments are performed so that the proposed algorithm can provide good results in the sense of subjective and objective views.