Journal of Convex Analysis 08 (2001), No. 2, 401--408
Copyright Heldermann Verlag 2001
Kernelled Quasidifferential for a Quasidifferentiable Function in Two-Dimensional Space
Yan Gao
School of Management, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China
Zun-Quan Xia
Dept. of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
Li-Wei Zhang
Dept. of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China
For a quasidifferentiable function defined on two-dimensional 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 two-dimensional case.
Keywords: Quasidifferential calculus, kernelled quasidifferential, minimal quasidifferential, nonsmooth analysis.
MSC: 52A20; 90C30
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