Abstract
We study a variational principle in which there is one common perturbation function ϕ for every proper lower semicontinuous extended real-valued function f defined on a metric space X. Necessary and sufficient conditions are given in order for the perturbed function f+ϕ to attain its minimum. In the case of a separable Banach space we obtain a specific principle in which the common perturbation function is, in addition, also convex and Hadamard-like differentiable. This allows us to provide applications of the principle to differentiability of convex functions on separable and more general Banach spaces.
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