System of Non-Linear Volterra Integral Equations in a Direct-Sum of Hilbert Spaces

Jabar Hassan; Haider  Majeed; Ghassan Ezzulddin  Arif

doi:10.46481/jnsps.2022.1021

Authors

Jabar Hassan
[email protected]
Department of Mathematics, College of Science, Salahaddin University - Erbil / Iraq
Haider Majeed Department of Mathematics, Tikrit University, College of Education for Pure Sciences, Tikrit/ Iraq
Ghassan Ezzulddin Arif Department of Mathematics, Tikrit University, College of Education for Pure Sciences, Tikrit/ Iraq

Keywords:

system of non-linear integral equations, Reproducing kernel Hilbert spaces, Fixed point theorem

Abstract

We use the contraction mapping theorem to present the existence and uniqueness of solutions in a short time to a system of non-linear Volterra integral equations in a certain type of direct-sum H[a; b] of a Hilbert space V[a; b]. We extend the local existence and uniqueness of solutions to the global existence and uniqueness of solutions to the proposed problem. Because the kernel function is a transcendental function in H[a; b] on the interval [a; b], the results are novel and very important in numerical approximation.

Dimensions

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