We establish a linear variational principle extending Deville–Godefroy–Zizler’s one. use this to prove that if $X$ is Banach space having property $(\alpha )$ of Schachermayer and $Y$ any space, then the set all str

We propose to study fragmentability of set-valued mappings not only for a given single mapping, but also for a sequence of mappings associated with the initial one. It turns out that this property underlies several variational principles, such as for example the Deville-Godefroy-Zizler variational principle and the Stegall variational principle, by providing a common path for proof.