In the article, we find the best possible parameters α 1 , α 2 , α 3 , β 1 , β 2 and β 3 such that the double inequalities (Formula Presented) hold all =a, b > 0 with a≠b, where (a, b) = (a + b)/2, H(a, b) = 2ab=(a + b), L(a, b) = (b - a)=(log b - log a) and TQ(a, b) = (Formula Presented) are the arithmetic, harmonic, logarithmic and Toader-Qi means of a and b, respectively. As applications, we present new bounds for the modified Bessel function of the first kind (Formula Pr...
