The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space

Pakhshan M. Hasan; Nejmaddin A. Sulaiman; Fazlollah Soleymani; Ali Akgül; Pakhshan M. Hasan; Nejmaddin A. Sulaiman; Fazlollah Soleymani; Ali Akgül

doi:10.3934/math.2020014

AIMS Mathematics

2020, Volume 5, Issue 1: 226-235. doi: 10.3934/math.2020014

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The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space

1.
Department of Mathematics, College of Education, Salahaddin University-Erbil, Iraq
2.
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
3.
Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, Turkey

Received: 20 July 2019 Accepted: 15 October 2019 Published: 05 November 2019
MSC : 35A01, 32K05

In this paper, a linear system of mixed Volterra-Fredholm integral equations is considered. The problem of existence and uniqueness of its solution is investigated and proved in a complete metric space by using the Banach fixed-point theorem. Also, an iterative method of fixed point type is used to approximate the solution of the system. The algorithm is applied on several examples. To show the accuracy of the results and the efficiency of the method, the approximate solutions are compared with the exact solutions.
- fixed point method,
- contraction mapping,
- Banach fixed-point (FP) theorem,
- mixed Volterra-Fredholm integral equation
Citation: Pakhshan M. Hasan, Nejmaddin A. Sulaiman, Fazlollah Soleymani, Ali Akgül. The existence and uniqueness of solution for linear system of mixed Volterra-Fredholm integral equations in Banach space[J]. AIMS Mathematics, 2020, 5(1): 226-235. doi: 10.3934/math.2020014

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Abstract

In this paper, a linear system of mixed Volterra-Fredholm integral equations is considered. The problem of existence and uniqueness of its solution is investigated and proved in a complete metric space by using the Banach fixed-point theorem. Also, an iterative method of fixed point type is used to approximate the solution of the system. The algorithm is applied on several examples. To show the accuracy of the results and the efficiency of the method, the approximate solutions are compared with the exact solutions.

References

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