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Almost Convex Functions: Conjugacy and Duality

In: Generalized Convexity and Related Topics

Author

Listed:
  • Radu Ioan Boţ

    (Chemnitz University of Technology)

  • Sorin-Mihai Grad

    (Chemnitz University of Technology)

  • Gert Wanka

    (Chemnitz University of Technology)

Abstract

Summary We prove that the formulae of the conjugates of the precomposition with a linear operator, of the sum of finitely many functions and of the sum between a function and the precomposition of another one with a linear operator hold even when the convexity assumptions are replaced by almost convexity or nearly convexity. We also show that the duality statements due to Fenchel hold when the functions involved are taken only almost convex, respectively nearly convex.

Suggested Citation

  • Radu Ioan Boţ & Sorin-Mihai Grad & Gert Wanka, 2007. "Almost Convex Functions: Conjugacy and Duality," Lecture Notes in Economics and Mathematical Systems, in: Generalized Convexity and Related Topics, pages 101-114, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-37007-9_5
    DOI: 10.1007/978-3-540-37007-9_5
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