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Paper's Title:

Lower and Upper Bounds for the Point-Wise Directional Derivative of the Fenchel Duality Map


M. Raissouli1,2, M. Ramezani3

1Department of Mathematics,
Science Faculty, Taibah University,
P.O. Box 30097, Zip Code 41477, Al Madinah Al Munawwarah,
Saudi Arabia.

2Department of Mathematics,
Science Faculty, Moulay Ismail University, Meknes,

3Department of Mathematics,
University of Bojnord, Bojnord,


In this paper, we introduce the point-wise directional derivative of the Fenchel duality map and we study its properties. The best lower and upper bounds of this point-wise directional derivative are also given. We explain how our functional results contain those related to the positive bounded linear operators.

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