• 대한수학회지
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• 제46권6호
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• pp.1319-1338
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• 2009

In this paper, using proximal-point mappings technique of Raccretive mappings and the property of the fixed point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of the system of parametric generalized quasi-variational inclusions involving R-accretive mappings in real uniformly smooth Banach space. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to parameters. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [3, 23, 24, 32, 33, 34].

• 충청수학회지
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• 제32권2호
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• pp.225-238
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• 2019

We show the boundedness and uniform Lipschitz stability for the solutions to the functional perturbed differential system $$y^{\prime}=f(t,y)+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^t}g(s,y(s),\;T_1y(s))ds+h(t,y(t),\;T_2y(t))$$, under perturbations. We impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s)$, $T_1y(s))ds$, $h(t,y(t)$, $T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of h-stability.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.381-403
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• 2022

The main goal of this research is to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.

• 대한수학회논문집
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• 제19권3호
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• pp.557-567
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• 2004

We prove the sufficient conditions for optimality in differential inclusion problem by using the value function. For this purpose, we assume at first that the value function is locally Lipschitz. Secondly, without this assumption, we use the viability theory.

• 한국산업정보학회논문지
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• 제11권5호
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• pp.62-66
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• 2006

We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1527-1534
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• 2010

In this paper, we consider nonsmooth optimization problem of which objective and constraint functions are locally Lipschitz. We establish sufficient optimality conditions and duality results for nonsmooth vector optimization problem given under nearly strict invexity and near invexity-infineness assumptions.

• 한국산업정보학회논문지
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• 제12권5호
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• pp.54-59
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• 2007

We abtain some stability results for a very general differential system using the method of cone valued vector Lyapunov functions and conversely some sufficient conditions for existence of such vector Lyapunov functions.

• East Asian mathematical journal
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• 제39권3호
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• pp.305-317
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• 2023

We establish the existence and uniqueness of Green functions in Lipschitz domains for stationary Stokes systems with Neumann boundary conditions. For the uniqueness, we impose a different normalization condition from that in Choi et al. (J. Math. Fluid Mech., 20(4):1745-1769, 2018).

• 대한수학회지
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• 제42권1호
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• pp.17-35
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• 2005

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

• 대한수학회보
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• 제45권3호
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.