Inequalities between Arithmetic-Geometric, Gini, and Toader Means

Table 1

Comparison of 𝒦(𝑟) with 𝐻(𝑟) for some 𝑟∈(0,1).

𝑟	𝒦(𝑟)	𝐻(𝑟)
0.1	1.574745561517⋯	1.574745561518⋯
0.2	1.586867847⋯	1.586867848⋯
0.3	1.608048620⋯	1.608048634⋯
0.4	1.639999866⋯	1.640000021⋯
0.5	1.685750355⋯	1.685751528⋯
0.6	1.750753803⋯	1.750760840⋯
0.7	1.845693998⋯	1.845732233⋯
0.8	1.995302778⋯	1.995519211⋯