Abstract
We prove the existence of solutions for the state depending convex sweeping processes in p-uniformly smooth and q-uniformly convex Banach spaces via new recent results on proximal analysis in reflexive smooth Banach spaces.
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The first author extends his appreciation to the Deanship of Scientific Research at King Saud University for funding the work through the research group project No. RGP-VPP-024.
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Bounkhel, M., Castaing, C. State Dependent Sweeping Process in p-Uniformly Smooth and q-Uniformly Convex Banach Spaces. Set-Valued Anal 20, 187–201 (2012). https://doi.org/10.1007/s11228-011-0186-8
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DOI: https://doi.org/10.1007/s11228-011-0186-8
Keywords
- Uniformly smooth and uniformly convex Banach spaces
- State dependent sweeping process
- Generalized projection
- Duality mapping