• Kyungpook Mathematical Journal
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• v.59 no.4
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• pp.703-723
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• 2019

In this paper, we consider a common solution of three problems in real Hilbert spaces: the Ky Fan inequality problem, the variational inequality problem and the fixed point problem for demicontractive single-valued and quasi-nonexpansive multi-valued mappings. To find the solution we present a new iterative algorithm and prove a strong convergence theorem under mild conditions. Moreover, we provide a numerical example to illustrate the convergence behavior of the proposed iterative method.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.667-680
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• 2020

Our paper deals with the following neutral nonlinear Levin-Nohel integro-differential with variable delay $${\frac{d}{dt}x(t)}+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t-r(t)}}^t}a(t,s)x(s)ds+{\frac{d}{dt}}g(t,x(t-{\tau}(t)))=0.$$ By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the existence of a unique periodic solution. An example is given to illustrate this work.

• School Mathematics
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• v.13 no.1
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• pp.175-187
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• 2011

The purpose of this study is to develop and utilize various kinds of mathematics teaching materials for gifted class in elementary school by utilizing polyominoes and a what-if-not strategy. Blokus is used to let students understand the characteristics of polyominoes, and omok is utilized to let them grasp interior point. Thus, the activities that utilized the new materials, blokus and omok, are developed to teach Pick's theorem. Besides, recreation activities were additionally prepared to provide education in an easy, intriguing and creative manner. The findings of the study is as follows: First, each of the materials was utilized in a different manner when the students engaged in basic and enrichment learning. Second, the mathematically gifted students were able to discover Pick's theorem in the course of utilizing the materials that contained recreational elements. Third, the students were taught to foster their problem-solving skills about area, girth and interior point by making use of the materials that were designed to be linked to each other. Fourth, existing programs were just designed to attain particular objects, to be conducted at a fixed time and to cater to particular graders. Fifth, when the students made problems by making use of the what if (not) strategy and the materials, they responded in diverse ways and were able to apply them.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.69-78
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• 2017

Shannon of the 5G smartphone and Fourier of the signal processing meet in the sampling theorem (2 times the highest frequency 1). In this paper, the initial Shannon Theorem finds the Shannon capacity at the point-to-point, but the 5G shows on the Relay channel that the technology has evolved into Multi Point MIMO. Fourier transforms are signal processing with fixed parameters. We analyzed the performance by proposing a 2N-1 multivariate Fourier-Jacket transform in the multimedia age. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^{\dot{+}}=nl_n$, where $A^{\dot{+}}$ is the transpose matrix of the element-wise inverse of A, that is, $A^{\dot{+}}=(a^{-1}_{kj})$, which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.12
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• pp.1759-1771
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• 2017

In this paper, an improved continuous integral variable structure systems(ICIVSS) with the prescribed control performance is designed for simple regulation controls of uncertain general linear systems. An integral sliding surface with an integral state having a special initial condition is adopted for removing the reaching phase and predetermining the ideal sliding trajectory from a given initial state to the origin in the state space. The ideal sliding dynamics of the integral sliding surface is analytically obtained and the solution of the ideal sliding dynamics can predetermine the ideal sliding trajectory(integral sliding surface) from the given initial state to the origin. Provided that the value of the integral sliding surface is bounded by certain value by means of the continuous input, the norm of the state error to the ideal sliding trajectory is analyzed and obtained in Theorem 1. A corresponding discontinuous control input with the exponential stability is proposed to generate the perfect sliding mode on the every point of the pre-selected sliding surface. For practical applications, the discontinuity of the VSS control input is approximated to be continuous based on the proposed modified fixed boundary layer method. The bounded stability by the continuous input is investigated in Theorem 3. With combining the results of Theorem 1 and Theorem 3, as the prescribed control performance, the pre specification on the error to the ideal sliding trajectory is possible by means of the boundary layer continuous input with the integral sliding surface. The suggested algorithm with the continuous input can provide the effective method to increase the control accuracy within the boundary layer by means of the increase of the $G_1$ gain. Through an illustrative design example and simulation study, the usefulness of the main results is verified.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.103-112
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• 2014

There are several theories to say that 'Mathematics is beautiful', but the typical one of them is a theory about the golden ratio. Often the golden ratio apt to be considered only as the geometric shapes or the simple number of ratio used in buildings and arts. However in this paper, we studied to consider the mathematical theories which are contained in their inside. In particular, we investigate the various expressions of the continued fraction which are represented by the golden ratio.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.25-32
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• 2011

In this paper, we study the existence and uniqueness of solutions for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions and forcing term with memory in n-dimensional fuzzy vector space ($E^n_N$, $d_{\varepsilon}$) by using Banach fixed point theorem. That is an extension of the result of Kwun et al. [9] to impulsive system.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.475-484
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• 2015

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If fⁿ(f³ - 1)f′ and gⁿ(g³ - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.79-87
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• 2009

This paper deals with the multipoint boundary value problem for one dimensional p-Laplacian $({\phi}_p(u'))'(t)$ + f(t,u(t)) = 0, $t{\in}$ (0, 1), subject to the boundary value conditions: u'(0) - $\sum\limits^n_{i=1}{\alpha_i}u({\xi}_i)$ = 0, u'(1) + $\sum\limits^n_{i=1}{\alpha_i}u({\eta}_i)$ = 0. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple (at least three) positive solutions to the above boundary value problem.

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.421-438
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• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.