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Non-linear operators and differentiability of Lipschitz functions
Mohammed Bachir, Sebastián Tapia-García
In this work we provide a characterization of distinct type of (linear and non-linear) maps between Banach spaces in terms of the differentiability of certain class of Lipschitz fu…
Asymmetric normed Baire space
Mohammed Bachir
We prove that an asymmetric normed space is never a Baire space if the topology induced by the asymmetric norm is not equivalent to the topology of a norm. More precisely, we show…
Porosity in the space of H{ö}lder-functions
Mohammed Bachir
Let (X, d) be a bounded metric space with a base point 0 X , (Y, ) be a Banach space and Lip 0 (X, Y) be the space of all -H{ö}lderfunctions that vanish at 0 X , eq…
Norm attaining operators and variational principle
Mohammed Bachir
We establish a linear variational principle extending the Deville-Godefroy-Zizler's one. We use this variational principle to prove that if is a Banach space having property $(…
Extending the Choquet theory: Trace convexity
Mohammed Bachir, Aris Daniilidis
We introduce the notion of trace convexity for functions and respectively, for subsets of a compact topological space. This notion generalizes both classical convexity of vector sp…
Index of symmetry and topological classification of asymmetric normed spaces
M Bachir, G. Flores
Let X, Y be asymmetric normed spaces and Lc(X, Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X, Y) is not a vector space. The a…