In this paper, we give several improvements of Mitrinović-Adamović's inequality and Lazarević's inequality. Our results show some interesting relationships between Mitrinović-Adamović's inequality and Lazarević's inequality. At the end of the paper, the improved Lazarević's inequality is applied to the sharpening of Wilker-type inequalities for hyperbolic functions.

In this paper, sharp bounds for cyclic sums of the ratio of the exradius to the sides of a triangle are established depending on the circumradius and inradius of the triangle. The best possible parameters for the expressions of bounds are derived. Moreover, an alternative bound for the ratio of the exradius to the sides of triangle, expressed by trigonometric functions, is also considered. MSC: 51M16; 26D05; 26D15