Codifferential calculus in normed spaces

Author: Dolgopolik M.  

Publisher: Springer Publishing Company

ISSN: 1072-3374

Source: Journal of Mathematical Sciences, Vol.173, Iss.5, 2011-03, pp. : 441-462

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Abstract

We study the approximation of nonsmooth functionals defined in a normed space. In particular, we employ the notion of codifferentiability for constructing an inhomogeneous approximation of the functional increment. We prove that the codifferentiable functions form a linear space closed under the main algebraic operations, pointwise maximum, and pointwise minimum. We also construct calculus of codifferentiable functions and prove the codifferentiability of the superposition of codifferentiable functions. Bibliography: 9 titles.