IJPAM: Volume 83, No. 3 (2013)

FOUR KINDS OF DIFFERENTIABLE MAPS

Cheng'en Yu1, Xiaolan Liu2
1,2School of Science
Sichuan University of Science and Engineering
Zigong, Sichuan, 643000, P.R. CHINA


Abstract. The B-differentiability of f is defined in general vector normed spaces, which is defined in finite dimensional Euclidean space (see [2]). Meanwhile, Gäteaux differentiability, Hadamard differentiability and Fréchet differentiability are also considered. In addition, srong Fréchet differentiability and strong Bouligand differentiability are also introduced. We present the relationships along these kinds of differentiable maps and give two examples to explain these relationships.

Received: October 30, 2012

AMS Subject Classification: 90C25, 90C33

Key Words and Phrases: Gäteaux differentiable; Hadamard differentiable; Fréchet differentiable; Bouligand-differentiable; Strong B-derivative; Strong F-derivative.

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DOI: 10.12732/ijpam.v83i3.7 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 3