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

Authors

  • Jabar Hassan 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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Published

2022-10-01

How to Cite

System of Non-Linear Volterra Integral Equations in a Direct-Sum of Hilbert Spaces. (2022). Journal of the Nigerian Society of Physical Sciences, 4(4), 1021. https://doi.org/10.46481/jnsps.2022.1021

Issue

Volume 4, Issue 4, November 2022

Section

Original Research
Copyright & Licensing

Copyright (c) 2022 Jabar Hassan, Haider, Ghassan

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

System of Non-Linear Volterra Integral Equations in a Direct-Sum of Hilbert Spaces. (2022). Journal of the Nigerian Society of Physical Sciences, 4(4), 1021. https://doi.org/10.46481/jnsps.2022.1021