• 전자공학회논문지SC
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• 제49권3호
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• pp.26-30
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• 2012

본 논문에서는 출력에 시간지연이 존재하는 이산 시간 비선형 시스템에 대한 상태관측기 설계방법을 제안한다. 비선형항에 대한 Lipschitz 조건을 가정하고 비선형항을 하나의 상태변수처럼 고려함으로써 비선형 이산시간 오차동역학방정식의 안정도 문제가 시간지연을 갖는 선형방정식의 안정도 문제로 변환될 수 있음을 보인다. 또한, 시간 지연 값에 의존적인 충분조건을 선형행렬 부등식을 이용하여 제시한다. 마지막으로 제안한 결과의 유효성을 증명하기 위하여 모의실험 예제를 제공한다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.203-221
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• 2007

We introduce a new two-point iterative method to approximate solutions of nonlinear operator equations. The method uses only divided differences of order one, and two previous iterates. However in contrast to the Secant method which is of order 1.618..., our method is of order two. A local and a semilocal convergence analysis is provided based on the majorizing principle. Finally the monotone convergence of the method is explored on partially ordered topological spaces. Numerical examples are also provided where our results compare favorably to earlier ones [1], [4], [5], [19].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권2호
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• pp.97-111
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• 2011

We provide a semilocal convergence result for approximating a solution of a singular system with constant rank derivatives, using Newton's method in an Euclidean space setting. Our approach uses more precise estimates and a combination of two Lipschitz-type conditions leading to the following advantages over earlier works [13], [16], [17], [29]: tighter bounds on the distances involved, and a more precise information on the location of the solution. Numerical examples are also provided in this study.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.83-99
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• 2019

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of ${\kappa}$-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.347-371
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• 2021

A plethora of applications from mathematical programmings, such as minimax, mathematical programming, penalization and fixed point problems can be framed as variational inequality problems. Most of the methods that used to solve such problems involve iterative methods, that is why, in this paper, we introduce a new extragradient-like method to solve pseudomonotone variational inequalities in a real Hilbert space. The proposed method has the advantage of a variable step size rule that is updated for each iteration based on previous iterations. The main advantage of this method is that it operates without the previous knowledge of the Lipschitz constants of an operator. A strong convergence theorem for the proposed method is proved by letting the mild conditions on an operator 𝒢. Numerical experiments have been studied in order to validate the numerical performance of the proposed method and to compare it with existing methods.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.917-933
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• 2021

In this paper, we investigate the behavior and sensitivity analysis of a solution set for a parametric generalized multi-valued nonlinear quasi-variational inclusion problem in a real Hilbert space. For this study, we utilize the technique of resolvent operator and the property of a fixed-point set of a multi-valued contractive mapping. We also examine Lipschitz continuity of the solution set with respect to the parameter under some appropriate conditions.

• Journal of applied mathematics & informatics
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• 제41권5호
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• pp.923-935
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• 2023

In this paper, we will discuss existence of solution of square-mean pseudo almost automorphic solution for fractional stochastic evolution equations driven by G-Brownian motion which is given as ^c₀D^𝛼_𝜌 Ψ_𝜌 = 𝒜(𝜌)Ψ_𝜌d𝜌 + 𝚽(𝜌, Ψ_𝜌)d𝜌 + ϒ(𝜌, Ψ_𝜌)d ⟨ℵ⟩_𝜌 + χ(𝜌, Ψ_𝜌)dℵ_𝜌, 𝜌 ∈ R. Furthermore, we also prove that solution of the above equation is unique by using Lipschitz conditions and Cauchy-Schwartz inequality. Moreover, examples demonstrate the validity of the obtained main result and we obtain the solution for an equation, and proved that this solution is unique.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.69-94
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• 2024

In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.225-258
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• 2024

In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.

• International Journal of Control, Automation, and Systems
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• 제4권4호
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• pp.448-455
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• 2006

This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.