On Generalized Classical Fréchet Derivatives in the Real Banach Space

In this work, we reviewed the Fréchet derivatives beginning with the basic definitions and touching most of the important basic results. These results include among others the chain rule, mean value theorem, and Taylor’s formula for differentiation. Obviously, having clarified that the Fréchet differential operators exist in the real Banach domain and that the operators are clearly continuous, we then in the last section for main results developed generalized results for the Fréchet derivatives of the chain rule, mean value theorem, and Taylor’s formula among others which become highly useful in the analysis of generalized Banach space problems and their solutions in Rn