• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1017-1029
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• 2010

In this paper we obtain a very general theorem of $\rho$-compatibility for three multivalued mappings, one of them from the class $\mathfrak{B}$. More exactly, we show that given a G-convex space Y, two topological spaces X and Z, a (binary) relation $\rho$ on $2^Z$ and three mappings P : X $\multimap$ Z, Q : Y $\multimap$ Z and $T\;{\in}\;\mathfrak{B}$(Y,X) satisfying a set of conditions we can find ($\widetilde{x},\;\widetilde{y}$) ${\in}$ $X\;{\times}\;Y$ such that $\widetilde{x}\;{\in}\;T(\widetilde{y})$ and $P(\widetilde{x}){\rho}\;Q(\widetilde{y})$. Two particular cases of this general result will be then used to establish existence theorems for the solutions of some general equilibrium problems.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.639-651
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• 2009

In this paper, we study a discrete Leslie-Gower one-predator two-prey model. By using the method of coincidence degree and some techniques, we obtain the existence of at least one positive periodic solution of the system. By linalization of the model at positive periodic solution and construction of Lyapunov function, sufficient conditions are obtained to ensure the global stability of the positive periodic solution. Numerical simulations are carried out to explain the analytical findings.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.307-318
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• 2013

In this paper, we introduce and study a new system of variational inclusions with B-monotone operators in Banach spaces. By using the proximal mapping associated with B-monotone operator, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm for this system of variational inclusions. The results presented in this paper extend and improve some known results in the literature.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.473-495
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• 2023

The use of mathematical modelling in the study of epidemiological disorders continues to grow substantially. In order to better support global policy initiatives and explain the possible consequence of an outbreak, mathematical models were constructed to forecast how epidemic illnesses spread. In this paper, fractional derivatives and (${\varpi}$ - F_𝓒)-contractions are used to explore the existence and uniqueness solutions of the novel coronavirus-19 model.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.1
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• pp.1-10
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• 1999

We consider the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear tune-Invariant plant such that a given closed loop transfer function is strictly sector bounded. We show that the standard $H{\infty}$ control problem and the $\tau$ -positive real control problem are special cases of sector bounded control problem. Necessary and sufficient conditions for the existence of a controller are obtained. The state-space representation for strictly proper controllers are given in terms of solutions to ARIs or AREs.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.1
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• pp.19-23
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• 2000

In this paper, we deal with the problem of designing guaranteed cost state feedback controller for the generalized time-varying delay systems with delayed state and control input. The generalized time delay system problems solved on the basis of LMI(linear matrix inequality) technique considering time-varying delays. The sufficient condition for the existence of controller and guaranteed cost state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be reformulated as LMI forms in terms of transformed variables. Therefore, all solutions of LMIs, guaranteed cost controller gain, and guaranteed cost are obtained at the same time. The proposed controller design method can be extended into the problem of robust guaranteed cost controller design method for parameter uncertain systems with time-varying delays easily.

• Journal of Institute of Control, Robotics and Systems
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• v.2 no.1
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• pp.1-4
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• 1996

This paper presents a state feedback $H^{\infty}$ controller design method for linear systems with delayed states and inputs. We derive a sufficient condition that the closed-loop system is asymptotically stable for all time-delays and that the $H^{\infty}$-norm of the closed-loop transfer function is less than or equal to some prescribed level $\gamma$. And we propose a sufficient condition for the existence of a state feedback $H^{\infty}$ controller using a form of linear matrix inequality(LMI). Furthermore, we show that the state feedback $H^{\infty}$ controllers can be obtained from solutions satisfying LMI.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.935-950
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• 2012

In this paper, we introduce and study a new system of generalized set-valued quasi-variational-like inclusions with (A, ${\eta}$)-accretive mapping in Banach spaces. By using the resolvent operator associated with (A, ${\eta}$)-accretive mappings, we construct a new iterative algorithm for approximating the solution of this system of variational inclusions. We also prove the existence of solutions and the convergence of the sequences generated by the algorithm in Banach spaces. The results presented in this paper extend and improve some known results in the literature.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.605-618
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• 2009

A stage-structured predator-prey system with time delay and Beddington-DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.