• The Pure and Applied Mathematics
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• v.18 no.1
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• pp.13-29
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• 2011

In this paper, we introduce the new concept of ${\omega}-D^*$-distance on a $D^*$-metric space and prove a non-convex minimization theorem which improves the result of Caristi[1], ${\'{C}}iri{\'{c}}$[2], Ekeland[4], Kada et al.[5] and Ume[8, 9].

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.565-585
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• 1996

In 1976, Caristi [1] established a celebrated fixed point theorem in complete metric spaces, which is a very useful tool in the theory of nonlinear analysis. Since then, several generalizations of the theorem were given by a number of authors: for instances, generalizations for single-valued mappings were given by Downing and Kirk [4], Park [11] and Siegel [13], and the multi-valued versions of the theorem were obtained by Chang and Luo [3], and Mizoguchi and Takahashi [10].

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.33-41
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• 2020

We introduced the concept of the 𝜖₀-density and the 𝜖₀-dense ace in [1]. This concept is related to the structure of employment. In addition to the double capacity theorem which was introduced in [1], we need the minimal dense subset. In this paper, we investigate a concept of the minimal 𝜖₀-dense subset in the Euclidean m dimensional space.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.437-442
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• 2014

In this paper we prove Ekeland's variational principle in the setting of locally complete spaces for lower semi continuous functions from above and bounded below. We use this theorem to prove Caristi's fixed point theorem in the same setting and also for lower semi continuous functions.

• 전기의세계
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• v.28 no.6
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• pp.61-77
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• 1979

This paper is concerned with minimization process of the binary logic function. This paper describes an algorithm called the SIMPLE TABLE METHOD that well suited to minimization a switching function of any number of variables. For the Simple Table construction, a theorem based upon the numerical properties of the logic function is derived from the relationships governing minterms of the given function. Finally the minimal sum of products can be obtained in terms of the Direct Method or the Indirect Method from the table and table characteristics derived from the Simple Table. The properties and table characteristics used in this paper are described. All the minterms of a switching function are manipulated only by decimal numbers, not binary numbers. Some examples are used as a vehicle to guide the readers who are familiar with the Karnaugh map and Quine-McCluskey tabular method to this New method. These examples not only treat how to handle Don't Care miterms but also show the multiple output functions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.411-432
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• 2021

In this paper, an inertial Halpern-type forward backward iterative algorithm for approximating solution of a monotone inclusion problem whose solution is also a fixed point of some nonlinear mapping is introduced and studied. Strong convergence theorem is established in a real Hilbert space. Furthermore, our theorem is applied to variational inequality problems, convex minimization problems and image restoration problems. Finally, numerical illustrations are presented to support the main theorem and its applications.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.55-60
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• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1639-1650
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• 2013

In this paper, a class of set-valued mappings is introduced, which is called uniformly same-order. For this sort of mappings, some minimax problems, in which the minimization and the maximization of set-valued mappings are taken in the sense of vector optimization, are investigated without any hypotheses of convexity.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.621-639
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• 2011

The purpose of this paper is to introduce a general iterative process by viscosity approximation method with parallel method to ap-proximate a common element of the set of solutions of a mixed equilibrium problem and of the set of common fixed points of a finite family of $k_i$-strict pseudo-contractions in a Hilbert space. We obtain a strong convergence theorem of the proposed iterative method for a finite family of $k_i$-strict pseudo-contractions to the unique solution of variational inequality which is the optimality condition for a minimization problem under some mild conditions imposed on parameters. The results obtained in this paper improve and extend the corresponding results announced by Liu (2009), Plubtieng-Panpaeng (2007), Takahashi-Takahashi (2007), Peng et al. (2009) and some well-known results in the literature.

• Journal of Electrical Engineering and Technology
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• v.12 no.1
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• pp.134-144
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• 2017

This paper presents an adaptive control strategy for the speed control of a four-phase switched reluctance motor (SRM) in automotive applications. The main objective is to minimize the torque ripples, despite the unstructured uncertainties, time-varying parameters and external load disturbances. The bound of perturbations is not required to be known in the developing of the proposed adaptive-based control method. In order to achieve a smooth control effort, some properties are incorporated and the proposed control algorithm is constructed using the Lyapunov theorem where the closed-loop stability and robust tracking are ensured. The effectiveness of the proposed controller in rejecting high perturbed load torque with smooth control effort is verified with comparing of an adaptive sliding mode control (ASMC) and validated with experimental results.