About differentiability of order one of quasiconvex functions onR n

  • J. P. Crouzeix
Contributed Papers

Abstract

This paper is devoted to the study of the different kinds of differentiability of quasiconvex functions onR n . For these functions, we show that Gâteaux-differentiability and Fréchet-differentiability are equivalent; we study the properties of the directional derivatives; and we show that if, for a quasiconvex function, the directional derivatives atx are all finite and two-sided, the function is differentiable atx.

Key Words

Quasiconvex functions Fréchet-differentiability Gâteau-differentiability quasidifferentiability generalized convexity 

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References

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Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • J. P. Crouzeix
    • 1
  1. 1.Department de Mathématiques AppliquéesUniversité de Clermont 2AubièreFrance

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