• 대한수학회보
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• 제45권4호
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• pp.635-644
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• 2008

In this paper, we prove that the equivalence between the convergence of Mann and Ishikawa iterations for the generalized Lipschitzian and $\Phi$-strongly pseudocontractive mappings in real uniformly smooth Banach spaces. Our results significantly generalize the recent known results of [B. E. Rhoades and S. M. Soltuz, The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitz operators, Int. J. Math. Math. Sci. 42 (2003), 2645.2651].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권2호
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• pp.99-109
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• 2007

Being complicated in computation, iteration of a nonlinear 1-dimensional mapping makes many interesting problems, one of which is about the change of the number of vertices under iteration. In this paper we investigate iteration of polygonal functions which each have only one vertex and give conditions under which the number of vertices either does not increase or has a bound under iteration.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.961-969
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• 2021

In this paper, we study the ∆-convergence and strong convergence of SP-iteration scheme involving a nonexpansive mapping in partially ordered hyperbolic metric spaces. Also, we give an example to support our main result and compare SP-iteration scheme with the Mann iteration and Ishikawa iteration scheme. Thus, we generalize many previous results.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2003년도 춘계종합학술대회
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• pp.753-757
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• 2003

본 논문에서는 반복복호 부호의 복호과정시 채널 적응적으로 반복복호수를 가변할 수 있는 효율적인 제어기법을 제안한다. 반복복호 부호는 반복구조를 가지며 그 특성상 반복복호수가 증가할수록 성능이 우수하게 향상된다. 그러나 반복복호수가 증가한 수록 복호과정시 적용된 알고리즘의 복잡도에 따라 다소 차이는 있지만 공통적으로 계산량의 증가를 가지게 되며 이는 복호지연시간 증가로 나타난다. 또한 일정 반복복호수 이상에 도달하게 되면 그 성능 변화가 거의 없는 오류마구(floor) 현상이 나타난다. 즉 성능변화가 없는 적절한 반복복호수 종료점을 찾아야 한다. 따라서 본 논문에서는 프레임 주기로 수신된 정보를 프레임 에러체크 지시자를 이용하여 채널의 변화를 감시하며 반복복호 부호의 반복복호수를 채널 적응적으로 승가, 감소할 수 있도록 제어하는 기법을 제안하였으며 결과적으로 반복구조를 가지는 부호의 방대한 계산량 감소와 이로 인한 복호지연 시간을 성능저하없이 효율적으로 단축시킬 수 있음을 보였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.347-350
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• 2004

In this paper, the acceleration is studied for the rigid-plastic FEM of metal forming simulation. In the FEM, the direct iteration and Newton-Raphson iteration are applied to obtain the initial solution and accurate solution respectively. In general, the acceleration scheme for the direct iteration is not used. In this paper, an Aitken accelerator is applied to the direct iteration. In the modified Newton-Raphson iteration, the step length or the deceleration coefficient is used for the fast and robust convergence. The step length can be determined by using the accelerator. The numerical experiments have been performed for the comparisons. The faster convergence is obtained with the acceleration in the direct and Newton-Raphson iterations.

• 호남수학학술지
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• 제39권1호
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• pp.1-25
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• 2017

In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.

• 대한수학회논문집
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• 제13권1호
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• pp.195-209
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• 1998

In this paper we present a new iteration method for solving optimization problems governed by partial differential equations. We generalize the existing methods such as simple gradient methods and pseudo-time methods to get an efficient iteration method. Numerical tests show that the convergence of the new iteration method is much faster than those of the pseudo-time methods especially when the parameter $\sigma$ in the cost functional is small.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.51-55
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• 2008

Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

• East Asian mathematical journal
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• 제18권2호
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• pp.261-270
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• 2002

We obtain the convergence of three-step iteration methods and generalized three-step iteration methods for quasi-contractive and generalized quasi-contractive mappings, respectively, in Banach spaces. Our results extend the corresponding results in [1], [4]-[6].

• East Asian mathematical journal
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• 제17권2호
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• pp.349-365
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• 2001

Let X be a real Banach space and $A:X{\rightarrow}2^X$ be an $\alpha$-strongly accretive operator. It is proved that if the duality mapping J of X satisfies Condition (I) with additional conditions, then the Ishikawa and Mann iteration processes with errors converge strongly to the unique solution of operator equation $z{\in}Ax$. In addition, the convergence of the Ishikawa and Mann iteration processes with errors for $\alpha$-strongly pseudo-contractive operators is given.