A Tauberian Theorem for the Type of an Entire Function

Theorem 1 and Corollary 1 of this note are refinements of a Tauberian theorem of R. C. Buck [2, p. 148]. From these I deduce Theorem 2 and Corollary 2 which are known to complete two results on the type of an integral function obtained by him [2, Corollaries 1, 2].