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Research Article | Open Access

A differential equation approach for solving implicit state-dependent convex sweeping processes in Banach spaces

Messaoud Bounkhel1( ), Bushra R. Al-sinan2
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
Department of Administrative and Financial Sciences, Nairiyah College, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia; Bushrar@uhb.edu.sa
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Abstract

In the setting of 2-uniformly convex Banach spaces, we prove the existence of solutions for a variant of the implicit state-dependent convex sweeping processes. Our approach is based on a differential equation associated with the generalized projection operator.

Keywords

uniformly smooth and uniformly convex Banach spacesdifferential equationsimplicit convex sweeping processgeneralized projectionduality mapping
CLC number: 34A60, 49J53

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AIMS Mathematics
Volume 9 Issue 1,
January 2024
Pages 2123-2136
DOI: 10.3934/math.2024106

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Cite this article:
Bounkhel M, Al-sinan BR. A differential equation approach for solving implicit state-dependent convex sweeping processes in Banach spaces. AIMS Mathematics, 2024, 9(1): 2123-2136. https://doi.org/10.3934/math.2024106

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Received: 13 September 2023
Revised: 10 December 2023
Accepted: 11 December 2023
Published: 15 January 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)