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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

Special Issues: Recent Advances in Fractional Calculus with Real World Applications

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.
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Keywords 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. AIMS Mathematics, 2020, 5(1): 226-235. doi: 10.3934/math.2020014


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