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

Messaoud Bounkhel; Bushra R. Al-sinan; Messaoud Bounkhel; Bushra R. Al-sinan

doi:10.3934/math.2024106

AIMS Mathematics

2024, Volume 9, Issue 1: 2123-2136. doi: 10.3934/math.2024106

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

Messaoud Bounkhel ^{1
,
,},
Bushra R. Al-sinan ²

1.
Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
2.
Department of Administrative and Financial Sciences, Nairiyah College, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia; Bushrar@uhb.edu.sa

Received: 13 September 2023 Revised: 10 December 2023 Accepted: 11 December 2023 Published: 20 December 2023
MSC : 34A60, 49J53

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.
- uniformly smooth and uniformly convex Banach spaces,
- differential equations,
- implicit convex sweeping process,
- generalized projection,
- duality mapping
Citation: Messaoud Bounkhel, Bushra R. Al-sinan. A differential equation approach for solving implicit state-dependent convex sweeping processes in Banach spaces[J]. AIMS Mathematics, 2024, 9(1): 2123-2136. doi: 10.3934/math.2024106

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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.

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