• Kyungpook Mathematical Journal
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• 제48권1호
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• pp.133-142
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• 2008

In this paper, we prove two strong convergence theorems for asymptotically nonexpansive mappings in Hibert spaces by hybrid methods. Our results extend and improve the recent ones announced by Nakajo, Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], Kim, Xu [T. H. Kim, H. K. Xu, Strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140-1152], Martinez-Yanes, Xu [C. Martinez-Yanes, H. K. Xu, Strong convergence of the CQ method for fixed point iteration processes, Nonlinear Anal. 64 (2006) 2400-2411] and some others.

• Bulletin of the Korean Chemical Society
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• 제11권5호
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• pp.450-455
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• 1990

Fifty eight obsidian artifacts and four obsidian source samples have been analyzed by instrumental neutron activation analysis. Artifact samples have been classified into classes by unsupervised learning techniques such as eigenvector projection and nonlinear mapping. The source samples have thereafter been connected to the classes by the supervised learning techniques such as SLDA and SIMCA so as to characterize each class by possible source sites. Some difference attributable to different nonlinear mapping techniques and the elemental effects on the separation between classes have been discussed.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.663-684
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• 2021

In this paper, we present some fixed point results for a general class of nonexpansive mappings in the framework of Banach space and also proposed a new iterative scheme for approximating the fixed point of this class of mappings in the frame work of uniformly convex Banach spaces. Furthermore, we establish some basic properties and convergence results for our new class of mappings in uniformly convex Banach spaces. Finally, we present an application to nonlinear integral equation and also, a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature with different choices of parameters and initial guesses. The results obtained in this paper improve, extend and unify some related results in the literature.

• 전자공학회논문지B
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• 제28B권9호
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• pp.739-746
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• 1991

This paper develops a modified multilayer perceptron architecture which speeds up learning as well as the net's mapping accuracy. In Phase I, a cluster partitioning algorithm like the Kohonen's self-organizing feature map or the leader clustering algorithm is used as the front end that determines the cluster to which the input data belongs. In Phase II, this cluster selects a subset of the hidden layer nodes that combines the input and outputs nodes into a subnet of the full scale backpropagation network. The proposed net has been applied to two mapping problems, one rather smooth and the other highly nonlinear. Namely, the inverse kinematic problem for a 3-link robot manipulator and the 5-bit parity mapping have been chosen as examples. The results demonstrate the proposed net's superior accuracy and convergence properties over the original backpropagation network or its existing improvement techniques.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.69-81
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• 2024

In this paper, we provide certain fixed point results for a generalized 𝛼-nonexpansive mapping, as well as a new iterative algorithm called SRJ-iteration for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and ∆-convergence theorem for generalized 𝛼-nonexpansive mapping in CAT(0) space. Finally, we present a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our results obtained in this paper improve, extend and unify results of Abbas et al. [10], Thakur et al. [22] and Piri et al. [19].

• 대한수학회논문집
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• 제10권2호
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• pp.301-304
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• 1995

Our main purpose in this paper is to discuss a new result on convergence of nonlinear contractive algorithms acting on different Banach spaces.

• Journal of Astronomy and Space Sciences
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• 제27권3호
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• pp.221-230
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• 2010

A 4+12+16 amplitude phase shift keying (APSK) modulation outperforms other 32-APSK modulations in a nonlinear additive white Gaussian noise (AWGN) channel because of its intrinsic robustness against AM/AM and AM/PM distortions caused by the nonlinear characteristics of a high-power amplifier. Thus, this modulation scheme has been adopted in the digital video broadcasting-satellite2 European standard. And it has been considered for high rate transmission of telemetry data on deep space communications in consultative committee for space data systems which provides a forum for discussion of common problems in the development and operation of space data systems. In this paper, we present an improved bits-to-symbol mapping scheme with a better bit error rate for a 4+12+16 APSK signal in a nonlinear AWGN channel and propose a simple signal detection algorithm for the 4+12+16 APSK from the presented bit mapping.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.329-341
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• 2005

In this paper, we introduce new random iterative sequences with errors approximating a unique random common fixed point for three random set-valued strongly pseudo-contractive mappings and show the convergence of the random iterative sequences with errors by using an approximation method in real uniformly smooth separable Banach spaces. As applications, we study the existence of random solutions for some kind of random nonlinear operator equations group in separable Hilbert spaces.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.219-231
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• 2009

We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

• 대한수학회논문집
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• 제25권2호
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• pp.313-325
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• 2010

General models for the relaxed proximal point algorithm using the notion of relative maximal accretiveness (RMA) are developed, and then the convergence analysis for these models in the context of solving a general class of nonlinear inclusion problems differs significantly than that of Rockafellar (1976), where the local Lipschitz continuity at zero is adopted instead. Moreover, our approach not only generalizes convergence results to real Banach space settings, but also provides a suitable alternative to other problems arising from other related fields.