• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.171-181
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• 1999

In this note, we will prove that the operator-valued function space integral as an operator from $L_p\;to\;L_{p'}$ (1

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.575-583
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• 2000

In this work, we solve the Fredholm-Volterra integral equation(FVIE) when the kernel takes a potential function form under given conditions. we represent this kernel in the Weber-sonin integral form.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.163-174
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• 1999

The purpose of this paper is to obtain the solution of Fredholm-Volterra integral equation with singular kernel in the space $L_2(-1, 1)\times C(0,T), 0 \leq t \leq T< \infty$, under certain conditions,. The numerical method is used to solve the Fredholm integral equation of the second kind with weak singular kernel using the Toeplitz matrices. Also the error estimate is computed and some numerical examples are computed using the MathCad package.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.165-182
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• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.323-334
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• 2017

In this paper, we propose a combined form for solving nonlinear interval Volterra-Fredholm integral equations of the second kind based on the modifying Laplace Adomian decomposition method. We find the exact solutions of nonlinear interval Volterra-Fredholm integral equations with less computation as compared with standard decomposition method. Finally, an illustrative example has been solved to show the efficiency of the proposed method.

• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.1-17
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• 2008

Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Hammerstein. Also, the normality and continuity of the integral operator are discussed. A numerical method is used to obtain a system of nonlinear integral equations in position. The solution is obtained, and many applications in one, two and three dimensionals are considered.

• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.407-416
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• 1999

In this paper we give some sufficient conditions for the existence and uniqueness of a continuous for the existence and uniqueness of a continuous slution of the system of Urysohn-Volterra equation with hysteresis.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.463-475
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• 2012

In this work, we investigate solving two-dimensional nonlinear Volterra integral equations of the first kind (2DNVIEF). Here we convert 2DNVIEF to the two-dimensional linear Volterra integral equations of the first kind (2DLVIEF) and then we solve it by using operational approach of the Tau method. But for solving the 2DLVIEF we convert it to an equivalent equation of the second kind and then by giving some theorems we formulate the operational Tau method with standard base for solving the equation of the second kind. Finally, some numerical examples are given to clarify the efficiency and accuracy of presented method.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.