期刊
COGENT MATHEMATICS & STATISTICS
卷 5, 期 1, 页码 -出版社
TAYLOR & FRANCIS AS
DOI: 10.1080/25742558.2018.1477543
关键词
convex functions; completely monotone; Stieltjes function; transcendental equation
Any function f from (0, infinity) onto (0, infinity) which is decreasing and convex has an inverse g which is positive, decreasing and convex. When f has some form of generalized convexity we determine additional convexity properties inherited by g. When f is positive, decreasing and p; q-convex, its inverse g is q; p-convex. Related properties which pertain when f is a Stieltjes function are developed. The results are illustrated with the Stieltjes function f (x) - arctano(1/sqrt(x)/sqrt(x) via a transcen-dental equation.
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