• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.63-74
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• 2004

Suppose that X is a real Banach space, K is a nonempty closed convex subset of X and T : $K\;\rightarrow\;K$ is a uniformly continuous ${\phi}$-hemicontractive operator or a Lipschitz ${\phi}-hemicontractive$ operator. In this paper we prove that under certain conditions the three-step iteration methods with errors converge strongly to the unique fixed point of T. Our results extend the corresponding results of Chang [1], Chang et a1. [2], Chidume [3]-[7], Chidume and Osilike [9], Deng [10], Liu and Kang [13], [14], Osilike [15], [16] and Tan and Xu [17].

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.15-23
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• 2008

This paper considers the problem of delay-dependent guaranteed cost controller design for uncertain neutral systems with distributed delays. The system under consideration is subject to norm-bounded time-varying parametric uncertainty appearing in all the matrices of the state-space model. By constructing appropriate Lyapunov functionals and using matrix inequality techniques, a state feedback controller is designed such that the resulting closed-loop system is not only robustly stable but also guarantees an adequate level of performance for all admissible uncertainties. Furthermore, a convex optimization problem is introduced to minimize a specified cost bound. By matrix transformation techniques, the corresponding optimal guaranteed controller can be obtained by solving a linear matrix inequality. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed approach.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.153-169
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• 2000

Let E be a real q-uniformly smooth Banach space which admits a weakly sequentially continuous duality map, and K a nonempty closed convex subset of E. Let T : K -> K be a mapping such that $F(T)\;=\;{x\;{\in}\;K\;:\;Tx\;=\;x}\;{\neq}\;0$ and (I - T) satisfies the accretive-type condition: $\;{\geq}\;{\lambda}$\mid$$\mid$x-Tx$\mid$$\mid$^2$, for all $x\;{\in}\;K,\;x^*\;{\in}\;F(T)$ and for some ${\lambda}\;>\;0$. The weak and strong convergence of the Ishikawa iteration method to a fixed point of T are investigated. An application of our results to the approximation of a solution of a certain linear operator equation is also given. Our results extend several important known results from the Mann iteration method to the Ishikawa iteration method. In particular, our results resolve in the affirmative an open problem posed by Naimpally and Singh (J. Math. Anal. Appl. 96 (1983), 437-446).

• East Asian mathematical journal
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• v.28 no.5
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• pp.597-604
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• 2012

Let C be a nonempty closed convex subset of real Hilbert space H and F = $\{S(t):t{\geq}0\}$ a nonexpansive self-mapping semigroup of C, and $f:C{\rightarrow}C$ is a fixed contractive mapping. Consider the process {$x_n$} : $$\{{x_{n+1}={\beta}_nx_n+(1-{\beta}_n)z_n\\z_n={\alpha}_nf(x_n)+(1-{\alpha}_n)S(t_n)P_C(x_n-r_nAx_n)$$. It is shown that {$x_n$} converges strongly to a common element of the set of fixed points of nonexpansive semigroups and the set of solutions of the variational inequality for an inverse strongly-monotone mapping which solves some variational inequality.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.6
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• pp.3121-3142
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• 2017

We present a method for 3D shape reconstruction of inextensible deformable surfaces from a single image. The key of our approach is to represent the surface as a 3D triangulated mesh and formulate the reconstruction problem as a sequence of Linear Programming (LP) problems. The LP problem consists of data constraints which are 3D-to-2D keypoint correspondences and shape constraints which are designed to retain original lengths of mesh edges. We use a closed-form method to generate an initial structure, then refine this structure by solving the LP problem iteratively. Compared with previous methods, ours neither involves smoothness constraints nor temporal consistency, which enables us to recover shapes of surfaces with various deformations from a single image. The robustness and accuracy of our approach are evaluated quantitatively on synthetic data and qualitatively on real data.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.4
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• pp.365-370
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• 2007

This paper studies an automation problem of a heating, a ventilating, and an air conditioning (HVAC) for the development of smart space. The HVAC system is described by the fuzzy system for the stability analysis and the controller design. The linear matrix inequalities (LMIs) conditions are derived for the stabilization problem of the closed-loop system under the analog control. Also, it is required to digitally redesign the pre-designed the analog HVAC control system in order to accomplish the remote control via web. It is shown the this digital redesign problem can be converted to the convex optimization problem with the LMI constraints. An example is provided to show the effectiveness of the proposed method.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.887-902
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• 2021

In this paper, we have introduced a generalized class Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼), i ∈ {0, 1} of harmonic univalent functions in unit disc 𝕌, a sufficient coefficient condition for the normalized harmonic function in this class is obtained. It is also shown that this coefficient condition is necessary for its subclass 𝒯 Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼). We further obtained extreme points, bounds and a covering result for the class 𝒯 Sⁱ_H (m, n, 𝛾, 𝜙, 𝜓; 𝛼). Also, show that this class is closed under convolution and convex combination. While proving our results, certain conditions related to the coefficients of 𝜙 and 𝜓 are considered, which lead to various well-known results.

• East Asian mathematical journal
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• v.25 no.4
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• pp.527-532
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• 2009

In this paper, we study the following extended generalized variational inequality problem, introduced by Noor (for short, EGVI) : Given a closed convex subset K in q-uniformly smooth Banach space B, three nonlinear mappings T : $K\;{\rightarrow}\;B^*$, g : $K\;{\rightarrow}\;K$, h : $K\;{\rightarrow}\;K$ and a vector ${\xi}\;{\in}\;B^*$, find $x\;{\in}\;K$, $h(x)\;{\in}\;K$ such that $\xi$, g(y)-h(x)> $\geq$ 0, for all $y\;{\in}\;K$, $g(y)\;{\in}\;K$. [see [2]: M. Aslam Noor, Extended general variational inequalities, Appl. Math. Lett. 22 (2009) 182-186.] By using sunny nonexpansive retraction $Q_K$ and the well-known Banach's fixed point principle, we prove existence results for solutions of (EGVI). Our results extend some recent results from the literature.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.3
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• pp.1-10
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• 1996

In this paper, the problem of simultaneously allocating servers and loadings of stations in a class of manufacturing systems modelled as network of queues is considered. The throughput function of the closed network of queues is demonstrated as a Schur convex function of server allocation, that is, increasing the server allocation vector under majorization increases the performance in the ship in terms of the throughput. It also reduces the congestion in the open network of queues in terms of reducing the total number of jobs in the sense of likelihood ratio ordering. These are the extentions of the numerical results of Green and Guha (1995) in the service system with independent M/M/c systems to the network of queues. The results can be used to support production planning in certain manufacturing systems.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.1-14
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• 2008

This paper presents a convex optimization method for observer-based mixed $H_2/H_{\infty}$ control design of linear systems with time-varying state, input and output delays. Delay-dependent sufficient conditions for the design of a desired observer-based control are given in terms of linear matrix inequalities (LMIs). An observer-based controller which guarantees asymptotic stability and a mixed $H_2/H_{\infty}$ performance for the closed-loop system of the linear system with time-varying delays is then developed. A Lyapunov-Krasovskii method underlies the observer-based mixed $H_2/H_{\infty}$ control design. A numerical example with simulation results illustrates the effectiveness of the methodology.