Titlebook: Basic Monotonicity Methods with Some Applications; Marek Galewski Textbook 2021 The Editor(s) (if applicable) and The Author(s), under exc

只看該作者 · 發(fā)表于 2025-3-23 19:03:02

Hermeneutics. Method and MethodologyIn this chapter we are interested in mappings that are derivatives of certain functionals. Given a functional defined on ., under suitable conditions, it is not a difficult task to investigate its differentiability.

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Hermeneutics. Method and MethodologyRecall that . is a real, separable, and reflexive Banach space. In this section we consider classical duality mapping together with its relation to the Riesz operator—in case we assume that we work in a Hilbert space.

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只看該作者 · 發(fā)表于 2025-3-24 19:01:14

On the Fenchel-Young Conjugate,The results collected here will help us in understanding the issues related to the invertibility of nonlinear mappings. If we recall that a derivative of a differentiable convex functional is a monotone mapping, there is no surprise that we mainly work with convex functionals here.

只看該作者 · 發(fā)表于 2025-3-25 00:17:15

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