On the set of Gateaux differentiability of the L1 norm

Document Type : Research Paper

Authors

1 Universidad del Valle, Departamento de Matematicas, Calle 13 100-00, Cali, Colombia

2 Universidad Santiago de Cali, Calle 5 62-00, Cali, Colombia

Abstract

Let (Ω,M,μ) be a measure space. In this paper, we establish the set of Gateaux differentiability for the usual norm of L1(Ω,μ) and the corresponding derivative formulae at each point in this set.

Keywords

Volume 14, Issue 1
January 2023
Pages 95-100
  • Receive Date: 27 June 2021
  • Revise Date: 06 August 2021
  • Accept Date: 21 August 2021