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Author Shapiro, I.
Source CiteSeerX
Content type Text
File Format PDF
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Directional Derivative ♦ Directional Differentiability ♦ Lipschitz Mapping ♦ Chain Rule ♦ General Framework ♦ Cr-directional Differentiability ♦ Various Definition ♦ Composite Mapping ♦ Topological Vector Space ♦ Finite-dimensional Space ♦ Homogeneous Mapping
Abstract Abstract. Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of G~teaux, Fr6chet, and Hadamard are singled out from the general framework of cr-directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed. Key Words. Directional derivatives, positively homogeneous mapping, locally Lipschitz mapping, chain rule. 1.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article