• Journal of the Chungcheong Mathematical Society
• /
• v.30 no.2
• /
• pp.273-284
• /
• 2017

In this paper, we study that the solutions to perturbed differential system $$y^{\prime}=f(t,y)+{{\displaystyle\smashmargin{2}{\int\nolimits_{t_0}}^{t}}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$$ have uniformly Lipschitz stability by imposing conditions on the perturbed part ${\int_{t0}^{t}}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$, and on the fundamental matrix of the unperturbed system y' = f(t, y) using integral inequalities.

• Journal of applied mathematics & informatics
• /
• v.32 no.5_6
• /
• pp.609-619
• /
• 2014

Nonsmooth equations with finitely many maximum functions is often used in the study of complementarity problems, variational inequalities and many problems in engineering and mechanics. In this paper, we consider the global convergence methods for nonsmooth equations with finitely many maximum functions. The steepest decent method and the smoothing gradient method are used to solve the nonsmooth equations with finitely many maximum functions. In addition, the convergence analysis and the applications are also given. The numerical results for the smoothing gradient method indicate that the method works quite well in practice.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.4
• /
• pp.749-759
• /
• 2012

A globally convergent algorithm for solving equilibrium problems is proposed. The algorithm is based on a proximal point algorithm (shortly (PPA)) with a positive definite matrix M which is not necessarily symmetric. The proximal function in existing (PPA) usually is the gradient of a quadratic function, namely, ${\nabla}({\parallel}x{\parallel}^2_M)$. This leads to a proximal point-type algorithm. We first solve pseudomonotone equilibrium problems without Lipschitzian assumption and prove the convergence of algorithms. Next, we couple this technique with the Banach contraction method for multivalued variational inequalities. Finally some computational results are given.

• East Asian mathematical journal
• /
• v.24 no.2
• /
• pp.191-199
• /
• 2008

In this paper, we introduce and studied a system of nonlinear projection equations with perturbation in Hilbert spaces. By using the fixed point theorem, we prove an existence of solution for this system of nonlinear projection equations. We construct an algorithm for approximating the solution of the system of nonlinear projection equations with perturbation and show that the iterative sequence generated by the algorithm converges to the solution of the system of nonlinear projection equations with perturbation under some suitable conditions.

• Journal of applied mathematics & informatics
• /
• v.6 no.1
• /
• pp.309-320
• /
• 1999

Models of single-server queues with vacations have been widely used to study the performance of many computer communi-cation and production systems. In this paper we analyze an M/G/1 queue with generalized vacations and exhaustive service. This sys-tem has been shown to possess a stochastic decomposition property. That is the customer waiting time in this system is distributed as the sum of the waiting time in a regular M/G/1 queue with no va-cations and the additional delay due to vacations. Herein a general formula for the additional delay is derived for a wide class of vacation policies. The formula is also extended to cases with multiple types of vacations. Using these new formulas existing results for certain vacation models are easily re-derived and unified.

• Journal of the Korean Mathematical Society
• /
• v.45 no.1
• /
• pp.1-27
• /
• 2008

We introduce a new concept of convex spaces and a multimap class K having certain KKM property. From a basic KKM type theorem for a K-map defined on an convex space without any topology, we deduce ten equivalent formulations of the theorem. As applications of the equivalents, in the frame of convex topological spaces, we obtain Fan-Browder type fixed point theorems, almost fixed point theorems for multimaps, mutual relations between the map classes K and B, variational inequalities, the von Neumann type minimax theorems, and the Nash equilibrium theorems.

• Kyungpook Mathematical Journal
• /
• v.62 no.3
• /
• pp.533-555
• /
• 2022

In this paper, we introduce a new algorithm for finding a solution of an equilibrium problem in a real Hilbert space. Our paper extends the single projection method to pseudomonotone variational inequalities, from a 2018 paper of Shehu et. al., to pseudomonotone equilibrium problems in a real Hilbert space. On the basis of the given algorithm for the equilibrium problem, we develop a new algorithm for finding a common solution of a equilibrium problem and fixed point problem. The strong convergence of the algorithm is established under mild assumptions. Several of fundamental experiments in finite (infinite) spaces are provided to illustrate the numerical behavior of the algorithm for the equilibrium problem and to compare it with other algorithms.