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Sharp bounds for the Toader-Qi mean in terms of harmonic and geometric means

Sharp bounds for the Toader-Qi mean in terms of harmonic and geometric means

In the article, we present the greatest values α and λ , and the least values β and μ in [0,1/2] such that the double inequalitieshold for all a,b > 0 with a = b , where H(a,b) = 2ab/(a + b) , G(a,b) = √ ab and T Q(a,b) …