Paper's Title:

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

Author(s):

M. Raissouli^1,2, 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,
Morocco.
E-mail: raissouli.mustapha@gmail.com
 

³Department of Mathematics,
University of Bojnord, Bojnord,
Iran.
E-mail: m.ramezani@ub.ac.ir

Abstract:

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.