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.
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Boţ, R.I., Grad, SM., Wanka, G. (2007). Almost Convex Functions: Conjugacy and Duality. In: Generalized Convexity and Related Topics. Lecture Notes in Economics and Mathematical Systems, vol 583. Springer, Berlin, Heidelberg . https://doi.org/10.1007/978-3-540-37007-9_5
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DOI: https://doi.org/10.1007/978-3-540-37007-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37006-2
Online ISBN: 978-3-540-37007-9
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