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On the Composition of Completely Monotonic Functions and Completely Monotonic Sequences and Related Questions
Author(s) -
Lorch Lee,
Newman Donald J.
Publication year - 1983
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-28.1.31
Subject(s) - monotonic function , citation , composition (language) , library science , mathematics , computer science , philosophy , linguistics , mathematical analysis
If, in addition, f(x) is continuous at x = a, then it is called completely monotonic over [a, b), with similar definitions for (a, b] and [a, b]. A function is absolutely monotonic if all its derivatives are non-negative. A detailed study of these concepts can be found, for example, in [11, Chapter IV]. Our chief concern here is for the standard case in which a = 0, b = + 00. For this, S. N. Bernstein established the following results (cf. [11, Theorems 12a and 12b, pp. 160-161]).