Abstract

This work reviews various aspects of the Frechet derivatives basically from the rst principle through some numerous results bordering on the basic theories. On displaying thorough proofs to the numerous analytical results, we hence showed that the Frechet derivatives is not a number at all but a linear operator and in the end we succeeded in establishing the existence of various generalized results on the Frechet derivatives.

Keywords and Phrases

Banach Space, Operator, Derivatives, Chain Rule, Mean Value Theorem and Implicit Function Theorem.

A.M.S. subject classification

46B25.

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