• 충청수학회지
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• 제24권2호
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• pp.393-400
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• 2011

In this paper we study h-stability for the linear impulsive equations using the notion of kinematical similarity and impulsive integral inequality.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.867-872
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• 1999

In this paper we study the stability theorems for nonlinear Fredholm-Volterra integral equations system.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.555-575
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• 2014

In this paper, we establish some new nonlinear integral inequalities of Gronwall-Bellman type. These inequalities generalize some famous inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some nonlinear ordinary differential and integral equations. More accurately we extend certain results which have been proved in A. Abdeldaim and M. Yakout [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.435-442
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• 2005

The mathematical properties of the sequentially operated systems are often described by integral equations. Reservoir system of a product and sequential probability ratio test (SPRT) are typical examples of sequentially operated systems. When the underlying random quantities follow Erlang distribution, a systematic method was developed to solve the integral equations. We extend the method to the cases having accrual functions of more general types. The solutions of the integral equations are represented as a linear combination of distribution functions, and the coefficients of the linear combination are obtained by solving linear system derived from the continuity condition of the solutions.

• Structural Engineering and Mechanics
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• 제83권1호
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• pp.67-77
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• 2022

In this study, frictionless continuous and discontinuous contact problems of a magneto-electro-elastic layer in the presence of the body force were discussed. The layer was indented by a rigid cylindrical insulating punch and supported by a rigid substrate without bond. Applying the Fourier integral transform technique, the general expressions of the problem were derived in the presence of body force. Thanks to the boundary conditions, the singular integral equations were obtained for both the continuous and the discontinuous contact cases. Gauss-Chebyshev integration formulas were used to transform the singular integral equations into a set of nonlinear equations. Contact width under the punch, initial separation distance, critical load, separation regions and contact stress under the punch and between the layer, and substrate were given as a result.

• 응용통계연구
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• 제18권1호
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• pp.57-66
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• 2005

본 연구에서는 얼랑(Erlang)분포의 규모모수에 대 한 축차확률비검정(SPRT)과 관련된 적분방정식의 정학한 해를 구하는 법을 살펴보기로 한다. 축차확률비검정에서 그 평균 표본 개수, 그리고 1종 오류 확률과 2종 오류 확률은 프레돔 형태의 적분 방정식으로 나타나게 된다. 이러한 적분 방정식은 보통 가우시안 쿼드러쳐(qudrature)를 이용하여 근사적으로 그 해를 구하는 것이 일반적이다. 얼랑분포의 경우 이러한 적분방정식의 해가 정확하게 구할 수 있음이 알려져 있다. 본 연구에서는 얼랑분포에서 그 해를 구하는 구체적 방법을 살펴보기로 한다.

• Korean Journal of Mathematics
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• 제23권3호
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• pp.491-502
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• 2015

A martingale is a mathematical model for a fair wager and the modern theory of martingales plays a very important and useful role in the study of the stochastic fields. This paper is devoted to investigate a martingale and a non-martingale on the several stochastic integral or differential equations. Specially, we show that whether the stochastic integral equation involving a standard Wiener process with the associated filtration is or not a martingale.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.305-320
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• 2012

In this paper, we study a class of integral boundary value problems for fractional differential equations. By using some fixed point theorems, the results of existence of at least three positive solutions for the boundary value problems are obtained.

• 대한수학회지
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• 제45권2호
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• pp.331-353
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• 2008

Some new nonlinear retarded integral inequalities of Gronwall-like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No.3, pp. 563-578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.

• 대한수학회지
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• 제45권1호
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• pp.121-136
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• 2008

Some new explicit bounds on the solutions to a class of new nonlinear retarded Volterra-Fredholm type integral inequalities in two independent variables are established, which can be used as effective tools in the study of certain integral equations. Some examples of application are also indicated.