Showing papers on "Gâteaux derivative published in 1971"
01 Jan 1971
TL;DR: In this paper, the differentiation and integration of nonlinear operators is discussed and a few examples taken from classical variational theory are presented. But the technique of defining a derivative from the gradient does not generalize for many reasons, not the least being that is actually backwards.
Abstract: Publisher Summary This chapter presents the differentiation and integration of nonlinear operators. The contemporary differentiation had its origin in the calculus of variations. It highlights a few examples taken from classical variational theory. A really vector space will usually be denoted by X or Y. However, Euclidean n-space is denoted by Rn and the real line by R. The chapter also explores the Gateaux and Frechet derivatives. The technique of defining a derivative from the gradient does not generalize for many reasons, not the least being that is actually backwards. The definition of the Gateaux derivative requires only the range space to have a topology defined on it.
34 citations