Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.8.2024.4.10

Volume 8, Issue 4, 1 August 2024, Pages 641-657

 

Abstract. In the theory of Banach spaces, the normalized duality mapping assumes a pivotal role. The analytic depiction of this mapping holds paramount significance in the associated analysis. Given that Bochner spaces serve as foundational underpinnings in stochastic variational analysis and stochastic optimizations, delving into the analytic representations of the normalized duality mapping becomes imperative, especially in uniformly convex and uniformly smooth Bochner spaces. The study of the analytic representations of normalized duality mapping contributes to our understanding of various geometric properties inherent in Bochner spaces. Leveraging the analytic representation of the normalized duality mapping, we establish and substantiate certain non-convex properties linked to this mapping in uniformly convex and uniformly smooth Bochner spaces.

 

How to Cite this Article:
L. Cheng, A. Khan, J. Li, C. Tammer, Normalized duality mappings and projections in Bochner spaces, J. Nonlinear Var. Anal. 8 (2024), 641-657.