Differentiability and Covering Constant for Duality Mappings in lp

Abstract: In this paper, we investigate the Gateaux differentiability of some duality mappings in the uniformly convex and uniformly smooth Banach space, which includes the normalized duality mapping as a special case, and it is denoted by J. We will introduce a general duality mapping and a generalized duality mapping. After the differentiability is proved, we find the explicit Gateaux and coderivative of J, and the duality mappings. By using coderivatives, we find the covering constants for these duality mappings, respectively. We also prove that the Gateaux derivative operator of the normalized duality mapping J has Lipchitz property.