<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.</p>
</abstract>

This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach spaces. We prove a theorem on the global convergence of successive approximations to the unique solution of the problems. An example is given to show the application of our result.

Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

Djillali Liabes University of Sidi Bel-Abbès

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

This paper discusses the global convergence of successive approximations methods for solving integro-differential equation via resolvent operators in Banach...

Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

Published Online: Mar 02, 2024

Page range: 44 - 55

Received: Jun 17, 2023

Accepted: Feb 24, 2024

DOI: https://doi.org/10.2478/awutm-2024-0003

Keywords
Integro-differential equation, mild solution, resolvent operator, global convergence, uniqueness, successive approximations

© 2024 Kattar Enada Bensatal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Existence and Successive Approximations of Mild Solution for Integro-differential Equations in Banach Spaces

Published Online: Mar 02, 2024

Page range: 44 - 55

Received: Jun 17, 2023

Accepted: Feb 24, 2024

DOI: https://doi.org/10.2478/awutm-2024-0003

KeywordsIntegro-differential equation, mild solution, resolvent operator, global convergence, uniqueness, successive approximations

© 2024 Kattar Enada Bensatal et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Integro-differential equation, mild solution, resolvent operator, global convergence, uniqueness, successive approximations