In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.
Published in Nonlinear Analysis. Theory, Methods & Applications 75 (2012), no. 3, 1124-1140. The original publication is available at http://www.sciencedirect.com/science/publication?issn=0362546X&volume=75&issue=3