A Converse of Taylor's Theorem for Functions on Banach Spaces

S. Dayal
1977 Proceedings of the American Mathematical Society  
The main results are the local representation theorems associating the local weak «-Taylor series expansion of a function defined on a Banach space to a local n-Taylor series expansion of the coefficients. These theorems are used to prove a converse of Taylor's theorem which uses weaker hyptohesis than used by others. Another useful application of the above results is done in [2] to study a class of functions called «-convex functions.
doi:10.2307/2041904 fatcat:2cahf3isfja5nnrolet75bkazm