Abstract In the work, the authors consider the Schur-convexity, the Schur-geometric convexity, and the Schur-harmonic convexity of two means defined by the inverse sine and tangent functions. They also apply these convexity properties to construct several inequalities for special means. These convexity properties correct and modify relevant results discussed in the paper D.-S. Chen, The Schur-convexity and inequality chains of two anti-trigonometric mean, Math. Pract. Theory 50 2020, 5, 268–275.
Yin et al. (Wed,) studied this question.