ABSTRACT
We continue the analysis of the extremum problems by means of the differentiation theory. The necessary condition of minimum at a point u of G a ^ $ \hat{\mathrm{a}} $ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152448/5968d418-c0e2-45a5-91c4-37245a5e7358/content/inline-math8_1.tif"/> teaux differentiable functional I on a convex subset U of a Banach space V is the variational inequality ⟨ I ′ ( u ) , v - u ⟩ ≥ 0 ∀ v ∈ U , $$ \begin{aligned} \langle I^{\prime }(u),v-u\rangle \, \ge \,0\;\forall v\in U, \end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315152448/5968d418-c0e2-45a5-91c4-37245a5e7358/content/un8_1.tif"/>
