ABSTRACT
1.1. Let X and Y be two spaces in a sequence {Hα } of real Hilbert spaces introduced in Chapter 1. Let Φ: X → Y be a non-linear operator with a domain D(Φ) ⊂ X which is assumed to be a convex set. Assume that Φ is continuously Gâteaux-differentiable. Then the formula holds true: () Φ ( u ) = Φ ( U 0 ) + ∫ 0 1 Φ ′ ( U 0 + t u ) d t u , u = U − U 0 , U , U 0 ∈ D ( Φ ) , https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315136707/b8efdbc7-0f66-4bda-8448-b1ca27e88da4/content/eq179.tif"/>
