• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.1017-1027
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• 2000

On the positive real number, we obtain the Hyers-Ulam stability and a stability in the sense of R. Ger for the generalized beta function g(x+p,y+q) = ${\varphi}(x,y)g(x,y)$ in the following settings: $$\mid$g(x+p,y+q)-{\varphi}(x,y)g(x,y)$\mid${\leq}{\delta}$ and $$\mid$\frac{g(x+p,y+q)}{\varphi(x,y)g(x,y)}-1$\mid${\leq}{\psi}(x,y). As a consequence we obtain stability theorems for the gamma functional equation and the beta functional equation.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.21-29
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• 2002

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measures. In this paper, we investigate the stability of the Feynman integral with respect to the measures.

• International Journal of Control, Automation, and Systems
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• v.4 no.2
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• pp.172-177
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• 2006

In the networked control system (NCS), the uncertain network-induced delay and nonlinear controlled object are the main problems, because they can degrade the performance of the control system and even destabilize it. In this paper, a class of uncertain and nonlinear networked control systems is discussed and its sufficient condition for the robust asymptotic stability is presented. Further, the maximum network-induced delay that insures the system stability is obtained. The Lyapunov and LMI theorems are employed to investigate the problem. The result of an illustrative example shows that the robust stability analysis is sufficient.

• Proceedings of the KIEE Conference
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• 1995.11a
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• pp.195-198
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• 1995

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is the most well-known and provides precise and rigorous theoretical backgrounds. However, tile conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, it is required to consider the damping effects. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. This method tan be utilized as a powerful tool to determine the region of attraction.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.518-521
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• 1994

Most of the theorems of nonlinear stability is based on the Lyapunov stability theory. The Lyapunov function method is most well-known and provides precise and rigorous theoretical backgrounds. However, the conventional approach to direct stability analysis has been performed without taking account of damping effects. For accurate stability analysis of nonlinear systems, the damping effects should be considered. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.7
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.233-241
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• 2003

The rolling schedule procedure has been an important part of the Enterprise Resource Planning (ERP) systems. The performance of production planning in an ERP system depends on the selection of the three parameters in rolling schedule procedure: frozen interval, replanning interval, and planning horizon (forecast window). This research investigated, in a theoretical approach, the combined impact of selections of those three parameters. The proven mathematical theorems provided guidance to re-duction of instability (nervousness) and to seek the optimal balance between stability and responsiveness of ERP systems. Further the theorems are extended to incorporate the cost structure.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.891-900
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• 2011

In this paper, we study the impulsive dynamic systems on time scales with initial time difference. By employing cone-valued Lyapunov functions, some comparison theorems and several practical ${\phi}_0$-stability criteria for impulsive system on time scales with initial time difference are obtained.