Absolute monotonicity of a family of functions related to Chen-Malesevic conjecture

In this paper, using the recurrence method and the absolute monotonicity rule, it is proved that the function Fq for q ? 1/2 defined on (0, 1) by Fq(x) = x arcsin x / (1 ? x2/(2q))q (arctanh x)2 is absolutely monotonic on (0, 1) if and only if q = 1/2, and ?F?q is absolutely monotonic on (0, 1) if and only if q ? 45/82. These give positive answers to Wang and Chen-Malesevic conjectures and yield several elegant results, such as, ln F1/2 and 1/Fq (q ? 45/82) are also absolutely monotonic on (0, 1).