• Kyungpook Mathematical Journal
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• 제62권1호
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• pp.89-106
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• 2022

We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.451-474
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• 2021

In this paper, we investigate a hybrid algorithm for finding zeros of the sum of maximal monotone operators and Lipschitz continuous monotone operators which is also a common fixed point problem for finite family of relatively quasi-nonexpansive mappings and split feasibility problem in uniformly convex real Banach spaces which are also uniformly smooth. The iterative algorithm employed in this paper is design in such a way that it does not require prior knowledge of operator norm. We prove a strong convergence result for approximating the solutions of the aforementioned problems and give applications of our main result to minimization problem and convexly constrained linear inverse problem.

• 대한수학회논문집
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• 제39권2호
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• pp.421-436
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• 2024

In this article, we propose a shrinking projection algorithm for solving a finite family of generalized equilibrium problem which is also a fixed point of a nonexpansive mapping in the setting of Hadamard manifolds. Under some mild conditions, we prove that the sequence generated by the proposed algorithm converges to a common solution of a finite family of generalized equilibrium problem and fixed point problem of a nonexpansive mapping. Lastly, we present some numerical examples to illustrate the performance of our iterative method. Our results extends and improve many related results on generalized equilibrium problem from linear spaces to Hadamard manifolds. The result discuss in this article extends and complements many related results in the literature.

• 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].

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.553-568
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• 2022

In this paper, we introduce and study two different iterative hybrid projection algorithms for solving a fixed point problem of nonexpansive mappings. The first algorithm is generated by the combination of the inertial method and the hybrid projection method. On the other hand, the second algorithm is constructed by the convex combination of three updated vectors and the hybrid projection method. The strong convergence of the two proposed algorithms are proved under very mild assumptions on the scalar control. For illustrating the advantages of these two newly invented algorithms, we created some numerical results to compare various numerical performances of our algorithms with the algorithm proposed by Dong and Lu [11].

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1179-1191
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• 2011

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a finite family of strict pseudocontractions and the solution set of pseudomonotone and Lipschitz-type continuous equilibrium problems. The scheme is based on the idea of extragradient methods and fixed point iteration methods. We show that the iterative sequences generated by this algorithm converge strongly to the common element in a real Hilbert space.

• 대한수학회논문집
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• 제25권3호
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• pp.419-426
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• 2010

In this paper, a three-step iterative method is considered for finding a common element in the set of fixed points of a non-expansive mapping and in the set of solutions of a variational inclusion problem in a real Hilbert space.

• 대한전자공학회논문지TC
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• 제43권11호
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• pp.95-117
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• 2006

본 논문에서는 IEEE 802.16e OFDMA/TDD 이동국 모뎀의 링크 성능과 복잡도 최적화를 위한 부동 및 고정 소수점 설계에 대하여 논한다. 부동 소수점 설계에서는 이동국 모뎀에서 하향링크 트래픽 채널의 채널 추정 방법을 제안하고, 모의실험을 통하여 최적의 알고리즘을 선정한다. 그리고 시간 및 주파수 동기화, Digital Front End와 CINR 추정 기법에 관하여 성능 향상과 시스템을 최적화하기 위한 알고리즘을 제안하고, 상향링크의 트래픽 채널과 제어 채널의 부동 소수점 설계 방법을 논한다. 제안된 알고리즘은 IEEE 802.16e OFDMA/TDD 시스템에 적용하여, 모의실험을 통한 성능을 Detection Probability, Mean Acqusition Time, PER 성능 그래프 등으로 그 우수성을 검증한다. 고정 소수점 설계에서는 부동 소수점 설계로부터 최적의 고정 소수점 설계를 위한 효율적인 방법론을 제시한다. 그리고 하향링크와 상향링크의 트래픽 채널, 시간 및 주파수 동기, DFE 블록을 고정 소수점 설계하고, 모의실험을 통하여 성능과 복잡도 간의 tradeoff 관계를 최적화한다.

• 대한수학회보
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• 제51권5호
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• pp.1527-1538
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• 2014

The purpose of this paper is to address the multiple split common fixed point problem. We present two different methods to approximate a solution of the problem. One is cyclic iteration method; the other is simultaneous iteration method. Under appropriate assumptions on the operators and iterative parameters, we prove both the proposed algorithms converge to the solution of the multiple split common fixed point problem. Our results generalize and improve some known results in the literatures.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2002년도 춘계학술발표논문집 (하)
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• pp.1033-1036
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• 2002

본 연구에서는 Newton 기법과 모멘트에 기초를 둔 fixed point 알고리즘의 신경망 기반 독립성분분석기법을 제안하였다. 여기서 Newton 기법은 함수의 접선에 기초를 둔 해를 구하는 방법으로 역혼합행렬의 빠른 경신을 위함이고, 모멘트는 접선을 구하는 과정에서 함수의 기울기변화 계산으로 발생하는 발진을 줄여 좀 더 빠른 학습을 위함이다. 제안된 기법을 $256{\times}256$ 픽셀(pixel)의 12개 지문영상으로부터 임의의 혼합행렬에 따라 발생되는 영상들을 각각 대상으로 시뮬레이션 한 결과, 기존의 Fixed point 알고리즘에 의한 결과보다 우수한 분리성능과 빠른 학습속도가 있음을 확인하였다.