• Proceedings of the Optical Society of Korea Conference
• /
• 2006.02a
• /
• pp.303-304
• /
• 2006

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.1
• /
• pp.85-93
• /
• 2007

In this paper we prove the existence of mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed point theorem.

• Communications of the Korean Mathematical Society
• /
• v.28 no.3
• /
• pp.559-569
• /
• 2013

The purpose of this paper is to establish existence, uniqueness and a variation of constant formula of solutions for semilinear partial functional differential equations with unbounded delays and nonlinear part involving integro differetial terms.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.1
• /
• pp.95-105
• /
• 2023

In the present paper, we introduce a new system of functional equations, known as orthogonal Pexider hom-derivation and Pexider hom-Pexider derivation (briefly, (Pexider) hom-derivation). Using the fixed point method, we investigate the stability of Pexider hom-derivations and (Pexider) hom-derivations on Banach algebras.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.63 no.4
• /
• pp.502-508
• /
• 2014

In this paper, a delay-dependent $H_{\infty}$ filtering problem is investigated for discrete-time delayed nonlinear systems which include a more general sector nonlinear function instead of employing the commonly used Lipschitz-type function. By using the Lyapunov-Krasovskii functional approach, a less conservative sufficient condition is established for the existence of the desired filter, and then, the corresponding solvability condition guarantee the stability of the filter with a prescribed $H_{\infty}$ performance level. Finally, two simulation examples are given to show the effectiveness of the proposed filtering scheme.

• Proceedings of the KIEE Conference
• /
• 1998.07b
• /
• pp.569-571
• /
• 1998

In this paper, a new method of conrolling chaotic nonlinear systems is proposed. Firstly, the dynamics of a chaotic nonlinear system is separated into a linear part and a nonlinear part. Secondly, the nonlinear part is approximated using a radial basis function network (RBFN) and canceled from the controlled system. Then, the resulting system has only the linear part added with very weak nonlinearity. Finally, a simple linear state feedback control law is designed for the linear part. In the meanwhile, a theorem justifying this concept is presented and proved. Comparing with the feedback linearization, the proposed method can be applied regardless of the functional form of the controlled dynamics. The proposed method is applied by simulation to the Duffing system and the Lorenz system and satisfactory results are obtained.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.445-450
• /
• 1998

In this paper, a robust nonlinear prediction-type controller (RNPC) is developed for the continuous time nonlinear system whose control objective is composed of system output and its desired value. The basic control law of RNPC is derived such that the future response of the system is first predicted by appropriate functional expansions and the control law minimizing the difference between the predicted and desired responses is then calculated. RNPC which involves two controls, i.e., the auxiliary and robust controls into the basic control, shows the stable closed loop dynamics of nonlinear system of any relative degree and provides the robustness to the nonlinear system with parameter/modeling uncertainty. Simulation tests for the position control of a two-link rigid body manipulator confirm the performance improvement and the robustness of RNPC.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.839-853
• /
• 2021

Let 𝕽ⁿ be an Euclidean space and g : 𝕽ⁿ → 𝕽ⁿ be a monotone and continuous mapping. Suppose the convex constrained nonlinear monotone equation problem x ∈ 𝕮 s.t g(x) = 0 has a solution. In this paper, we construct an inertial-type algorithm based on the three-term derivative-free projection method (TTMDY) for convex constrained monotone nonlinear equations. Under some standard assumptions, we establish its global convergence to a solution of the convex constrained nonlinear monotone equation. Furthermore, the proposed algorithm converges much faster than the existing non-inertial algorithm (TTMDY) for convex constrained monotone equations.

• Environmental Engineering Research
• /
• v.19 no.3
• /
• pp.247-253
• /
• 2014

The aim of this study was to characterize quintinite in fluoride removal from aqueous solutions, using batch experiments. Experimental results showed that the maximum adsorption capacity of fluoride to quintinite was 7.71 mg/g. The adsorption of fluoride to quintinite was not changed at pH 5-9, but decreased considerably in highly acidic (pH < 3) and alkaline (pH > 11) solution conditions. Kinetic model analysis showed that among the three models (pseudo-first-order, pseudo-second-order, and Elovich), the pseudo-second-order model was the most suitable for describing the kinetic data. From the nonlinear regression analysis, the pseudo-second-order parameter values were determined to be $q_e=0.18mg/g$ and $k_2=28.80g/mg/hr$. Equilibrium isotherm model analysis demonstrated that among the three models (Langmuir, Freundlich, and Redlich-Peterson), both the Freundlich and Redlich-Peterson models were suitable for describing the equilibrium data. The model analysis superimposed the Redlich-Peterson model fit on the Freundlich fit. The Freundlich model parameter values were determined from the nonlinear regression to be $K_F=0.20L/g$ and 1/n=0.51. This study demonstrated that quintinite could be used as an adsorbent for the removal of fluoride from aqueous solutions.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.2
• /
• pp.497-520
• /
• 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).