


Paper's Title:
Some Functional Inequalities for the Geometric Operator Mean
Author(s):
Mustapha Raissouli
Taibah University, Faculty of Sciences,
Department of Mathematics,
Al Madinah Al Munawwarah, P.O.Box 30097,
Kingdom of Saudi Arabia.
Abstract:
In this paper, we give some new inequalities of functional type for the power geometric operator mean involving several arguments.
Paper's Title:
Lower and Upper Bounds for the PointWise Directional Derivative of the Fenchel Duality Map
Author(s):
M. Raissouli^{1,2}, M. Ramezani^{3}
^{1}Department
of Mathematics,
Science Faculty, Taibah University,
P.O. Box 30097, Zip Code 41477, Al Madinah Al Munawwarah,
Saudi Arabia.
^{2}Department
of Mathematics,
Science Faculty, Moulay Ismail University, Meknes,
Morocco.
Email:
raissouli.mustapha@gmail.com
^{3}Department
of Mathematics,
University of Bojnord, Bojnord,
Iran.
Email: m.ramezani@ub.ac.ir
Abstract:
In this paper, we introduce the pointwise directional derivative of the Fenchel duality map and we study its properties. The best lower and upper bounds of this pointwise directional derivative are also given. We explain how our functional results contain those related to the positive bounded linear operators.
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