
Journal of Convex Analysis 08 (2001), No. 2, 401408 Copyright Heldermann Verlag 2001 Kernelled Quasidifferential for a Quasidifferentiable Function in TwoDimensional Space Yan Gao School of Management, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China ZunQuan Xia Dept. of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China LiWei Zhang Dept. of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China For a quasidifferentiable function defined on twodimensional space in the sense of Demyanov and Rubinov it is proved that the pair of the intersection of the sums of the subdifferentials and superdifferentials for all quasidifferentials, and the intersection of the differences of the subdifferentials and superdifferentials for all quasidifferentials is a quasidifferential of the function. It is shown that this way can be viewed as an approach to determining or choosing a representative for the equivalent class of quasidifferentials for a quasidifferentiable function at a point, in the twodimensional case. Keywords: Quasidifferential calculus, kernelled quasidifferential, minimal quasidifferential, nonsmooth analysis. MSC: 52A20; 90C30 [ Fulltextpdf (290 KB)] 