Sharp two parameter bounds for logarithmic and arithmetic-geometric means

Yu-Ming Chu, Ye-Fang Qiu, Miao-Kun Wang +1

For fixed $s\ge 1$ and $t_1,t_2\in (0,1/2)$ we prove that the inequalities $G^s(t_{1}a+(1-t_1)b,t_{1}b+(1-t_1)a)A^{1-s}(a,b)>AG(a,b)$ and $G^{s}(t_{2}a+(1-t_{2})b,t_{2}b+…