• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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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].

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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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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• v.26 no.5
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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.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2003.05a
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• pp.753-757
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• 2003

In this paper, We propose an efficient iteration decoding control method with variable iteration decoding for iteration codes decoding. As the number of iterations increases, the bit error rate and frame error rate of the decoder decrease and the incremental improvement gradually diminishes. However, as the iteration decoding number is increase, it require much delay and amount of processing for decoding. Thus we propose variable iteration control method to adapt variation of channel using Frame Error-Check indicator. Therefore, the CRC method requires the fewest iterations and less computation than the CE method and the SCR methods.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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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.

• Honam Mathematical Journal
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• v.39 no.1
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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.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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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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• v.16 no.1
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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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• v.18 no.2
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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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• v.17 no.2
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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.