In the paper, with aid of the Maclaurin power series expansions of the hyperbolic sine and cosine functions, and in light of stratification method invented and applied by Malesevic and his coauthors, the authors establish several inequalities for bounding the sums of the hyperbolic functions sinhc(2x), tanhc x, and their reciprocals. These inequalities are extensions of the Huygens-type inequalities.
Li et al. (Thu,) studied this question.