OnG-semidifferentiable functions in Euclidean spaces

  • N. D. Yen
Contributed Papers


We give a criterion for a functionf:R n →R to be upperG-semidifferentiable in the sense of Ref. 1 at a point\(\bar x \in R^n \). Using this result, we describe upperG-semiderivatives whenG is, for instance, one of the following basic classes of homogeneous functions: the set of all continuous positively homogeneous functions, the set of differences of two sublinear functions, and the set of sublinear functions. As a result, connections between upperG-semidifferentiability and the concepts of differentiability in Refs. 2–4 are obtained.

Key Words

Homogeneous functions Dini and Dini-Hadamard directional derivatives upperG-semiderivatives 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • N. D. Yen
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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