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

1977
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Proceedings of the American Mathematical Society
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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