• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.471-497
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• 2022

In this paper, we study a system of nonlinear wave equations associated with the helical flows of Maxwell fluid. By constructing a N-order iterative scheme, we prove the local existence and uniqueness of a weak solution. Furthermore, we show that the sequence associated with N-order iterative scheme converges to the unique weak solution at a rate of N-order.

• 한국수학사학회지
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• 제18권3호
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• pp.107-117
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• 2005

본 논문에서는 선형 헨스톡 적분방정식과 조금 다른 선형 근사 헨스톡 적분방정식을 소개하고, 어떤 적분방정식이 헨스톡 적분의미에서는 해를 갖지 않지만 근사 헨스톡 적분의미에서는 해를 갖는 예를 보이고 더욱 더 우리는 선형 근사 헨스톡 적분방정식의 해의 존재성과 유일성에 대하여 연구하였다.

• 한국CDE학회논문집
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• 제7권4호
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• pp.219-232
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• 2002

In numerically controlled(NC) machining simulation, a Z-map has been used frequently for representing a workpiece. Since the Z-map is usually represented by a set of Z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when an APT-type tool moves along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these characteristics, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation can be achieved by updating the Z-map properly. Our method can provide more accurate results with a little more processing time, in comparison with the previous closed-form solution.

• Journal of applied mathematics & informatics
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• 제42권4호
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• pp.749-759
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• 2024

In this manuscript, we formulate the notion of Ω(H, θ)-contraction on a self mapping f : W → W, this contraction based on the concept of Ω-distance mappings equipped on G-metric spaces together with the concept of H-simulation functions and the class of Θ-functions, we employ our new contraction to unify the existence and uniqueness of some new fixed point results. Moreover, we formulate a numerical example and a significant application to show the novelty of our results; our application is based on the significant idea that the solution of an equation in a certain condition is similar to the solution of a fixed point equation. We are utilizing this idea to prove that the equation, under certain conditions, not only has a solution as the Intermediate Value Theorem says but also that this solution is unique.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• Industrial Engineering and Management Systems
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• 제1권1호
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• pp.29-45
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• 2002

In this study, we consider infinite supply of raw materials and backlogged demands as given two boundary conditions. And we need not make any specific assumptions about the inter-arrival of external demand and service time distributions. We propose a numeric model and an algorithm in order to compute the first two moments of inter-departure process. Entropy enables us to examine the convergence of this process and to derive measurable relations of this process. Also, lower bound on the variance of inter-departure process plays an important role in proving the existence and uniqueness of an optimal solution for a numeric model and deriving the convergence order of augmented Lagrange multipliers method applied to a numeric model. Through these works, we confirm some structural properties and numeric examples how the validity and applicability of our study.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권4호
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• pp.271-287
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• 2008

This paper deals with American call and put options. Determining the fair price and the free boundary of an American option is a very difficult problem since they depends on each other. This paper presents numerical algorithms of finite element method based on the three-level scheme to compute both the price and the free boundary. One algorithm is designed for American call options and the other one for American put options. These algorithms are formulated on the system of the Jamshidian equation for the option price and the free boundary. Here, the Jamshidian equation is of a kind of the nonhomogeneous Black-Scholes equations. We prove the existence and uniqueness of the numerical solution by the Lax-Milgram lemma and carried out extensive numerical experiments to compare with various methods.

• 품질경영학회지
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• 제11권2호
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• pp.2-9
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• 1983

As will be seen, this paper is tries that the research on the mathematical structure of Markov process and Markovian sequential decision process (the policy improvement iteration method,) moreover, that it analyze the logic and the characteristic of behavior of mathematical model of Markov process. Therefore firstly, it classify, on research of mathematical structure of Markov process, the forward equation and backward equation of Chapman-kolmogorov equation and of kolmogorov differential equation, and then have survey on logic of equation systems or on the question of uniqueness and existence of solution of the equation. Secondly, it classify, at the Markovian sequential decision process, the case of discrete time parameter and the continuous time parameter, and then it explore the logic system of characteristic of the behavior, the value determination operation and the policy improvement routine.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.171-183
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• 2005

In this paper, we introduce and study a class of general strongly nonlinear quasivariational inequalities in Hilbert spaces. We prove the existence and uniqueness of solution and convergence of the perturbed the three-step iterative sequences with errors for this kind of general strongly nonlinear quasivariational inquality problems involving relaxed Lipschitz, relaxed monotone, and strongly monotone mappings. Our results extend, improve, and unify many known results due to Liu-Ume-Kang, Kim-Kyung, Zeng and others.

• Journal of applied mathematics & informatics
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• 제41권3호
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• pp.487-510
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• 2023

We propose a mathematical model which describes the frictional contact between a piezoelectric body and an electrically conductive foundation. The behavior of the material is described with a linearly electro-viscoelastic constitutive law with long term memory. The mechanical process is dynamic and the electrical conductivity coefficient depends on the total slip rate, the friction is modeled with Tresca's law which the friction bound depends on the total slip rate with taking into account the electrical conductivity of the foundation both. The main results of this paper concern the existence and uniqueness of the weak solution of the model; the proof is based on results for second order evolution variational inequalities with a time-dependent hemivariational inequality in Banach spaces.