Second-order sufficient conditions for error bounds in banach spaces

Abstract

Recently, Huang and Ng presented second-order sufficient conditions for error bounds of continuous and Gâteaux differentiate functions in Banach spaces. Wu and Ye dropped the assumption of Huang and Ng on Gâteaux differentiability but required the space to be a Hilbert space. We carry on this research in two directions. First we extend Wu and Ye's result to some non-Hilbert spaces; second, same as Huang and Ng, we work on Banach spaces but provide different second-order sufficient conditions that may allow the function to be non-Gâteaux differentiate. © 2006 Society for Industrial and Applied Mathematics.