• 대한수학회보
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• 제50권3호
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• pp.1007-1020
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• 2013

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotically nonexpansive mappings on an arbitrary normed space. Our results generalize and extend several known results.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• 한국멀티미디어학회논문지
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• 제18권11호
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• pp.1289-1301
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• 2015

Pedestrian detection (PD) is an essential task in various applications and sliding window-based methods utilizing HOG (Histogram of Oriented Gradients) or HOG-like descriptors have been shown to be very effective for accurate PD. However, due to exhaustive search across images, PD methods based on sliding window usually require heavy computational time. In this paper, we propose a real-time PD method for embedded visual surveillance with fixed backgrounds. The proposed PD method employs HOG descriptors as many PD methods does, but utilizes selective search so that it can save processing time significantly. The proposed selective search is guided by restricting searching to candidate regions extracted from Adaptive Gaussian Mixture Model (AGMM)-based background subtraction technique. Moreover, approximate computation of HOG descriptor and implementation in fixed-point arithmetic mode contributes to reduction of processing time further. Possible accuracy degradation due to approximate computation is compensated by applying an appropriate one among three offline trained SVM classifiers according to sizes of candidate regions. The experimental results show that the proposed PD method significantly improves processing speed without noticeable accuracy degradation compared to the original HOG-based PD and HOG with cascade SVM so that it is a suitable real-time PD implementation for embedded surveillance systems.

• East Asian mathematical journal
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• 제28권5호
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• pp.561-567
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• 2012

The approximate solvability of a generalized system for relaxed cocoercive extended general variational inequalities is studied by using the project operator technique. The results presented in this paper are more general and include many previously known results as special cases.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.389-401
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• 2015

We will show the general solution of the functional equation f(x + ay) + f(x − ay) + 2(a² − 1)f(x) = a²f(x + y) + a²f(x − y) + 2a²(a² − 1)f(y) and investigate the stability of quartic Lie *-derivations associated with the given functional equation.

• 대한수학회논문집
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• 제30권3호
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• pp.209-219
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• 2015

In this article, we first give metric version of an iteration scheme of Agarwal et al. [1] and approximate fixed points of two finite families of nonexpansive mappings in hyperbolic spaces through this iteration scheme which is independent of but faster than Mann and Ishikawa scheme. Also we consider case of three finite families of nonexpansive mappings. But, we need an extra condition to get convergence. Our convergence theorems generalize and refine many know results in the current literature.

• 한국CDE학회논문집
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• 제21권4호
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• pp.389-396
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• 2016

The necessity for environment-friendly material development has emerged in the recent automotive field due to stricter regulations on fuel economy and environmental concerns. Accordingly, the automotive industry is paying attention to carbon fiber reinforced plastic (CFRP) material with high strength and stiffness properties while the lightweight. In this study, we determine a shape of lower control arm (LCA) for maximizing the strength and stiffness by optimizing the thickness of each layer when the stacking angle is fixed due to the CFRP manufacturing problems. Composite materials are laminated in the order of $0^{\circ}$, $90^{\circ}$, $45^{\circ}$, and $-45^{\circ}$ with a symmetrical structure. For the approximate optimal design, we apply a sequential two-point diagonal quadratic approximate optimization (STDQAO) and use a process integrated design optimization (PIDO) code for this purpose. Based on the physical properties calculated within a predetermined range of laminate thickness, we perform the FEM analysis and verify whether it satisfies the load and stiffness conditions or not. These processes are repeated for successive improved objective function. Optimized CFRP LCA has the equivalent stiffness and strength with light weight structure when compared to conventional aluminum design.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.137-162
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• 2024

This paper consists of two significant aims. The first aim of this paper is to establish the criteria for the existence of solutions to nonlinear Volterra-Fredholm (V-F) fractional integral equations on [0, L], where 0 < L < ∞. The fractional integral is described here in the sense of the Katugampola fractional integral of order λ > 0 and with the parameter β > 0. The concepts of the fixed point theorem and the measure of noncompactness are used as the main tools to prove the existence of solutions. The second aim of this paper is to introduce a computational method to obtain approximate numerical solutions to the considered problem. This method is based on the Fibonacci wavelets with collocation technique. Besides, the results of the error analysis and discussions of the accuracy of the solutions are also presented. To the best knowledge of the authors, this is the first computational method for this generalized problem to obtain approximate solutions. Finally, two examples are discussed with the computational tables and convergence graphs to interpret the efficiency and applicability of the presented method.

• 한국정보통신학회논문지
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• 제11권1호
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• pp.46-55
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• 2007

다음은 부동소수점 역수 및 역제곱근 계산에 많이 사용하는 뉴톤-랍손 알고리즘은 일정한 횟수의 곱셈을 반복하여 계산한다. 본 논문에서는 뉴톤-랍손 알고리즘의 반복 과정의 오차를 예측하여 오차가 정해진 값보다 작아지는 시점까지 반복 연산하는 개선된 뉴톤-랍손 알고리즘을 제안한다. 본 논문에서 제안한 알고리즘은 입력 값에 따라서 곱셈 횟수가 다르므로, 평균 곱셈 횟수를 계산하는 방식을 유도하고, 여러 크기의 근사 테이블에서 단정도실수 및 배정도실수의 역수 및 역제곱근 계산에 필요한 평균 곱셈 횟수를 산출한다. 이들 평균 곱셈 횟수를 종래 알고리즘과 비교하여 본 논문에서 제안한 알고리즘의 우수성을 증명한다. 본 논문에서 제안한 알고리즘은 오차가 일정한 값보다 작아질 때까지만 반복 연산을 수행하므로 역수 및 역제곱근 계산기의 성능을 높일 수 있고 최적의 근사 테이블을 구성할 수 있다. 본 논문의 연구 결과는 디지털 신호처리, 컴퓨터 그라픽스, 멀티미디어, 과학 기술 연산 등 부동소수점 계산기가 사용되는 분야에서 폭 넓게 사용될 수 있다.

• 대한수학회논문집
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• 제22권2호
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• pp.247-258
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• 2007

In this paper a new class of system of generalized nonlinear variational inequalities involving strongly monotone, relaxed co coercive and relaxed generalized monotone mappings in Hilbert spaces is introduced and studied. Based on the projection method, an equivalence between the system of generalized nonlinear variational inequalities and the fixed point problem is established, which is used to suggest some new iterative algorithms for computing approximate solutions of the system of generalized nonlinear variational inequalities. A few sufficient conditions which ensure the existence and uniqueness of solution of the system of generalized nonlinear variational inequalities are given, and the convergence analysis of iterative sequences generated by the algorithms are also discussed.