Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-logarithmic measures known as triangular discrimination, Hellingar’s divergence and symmetric chi-square divergence. However, in 2003, Eve studied ...

by using generalized salagean differential operator a newclass of univalent holomorphic functions with fixed finitely manycoefficients is defined. coefficient estimates, extreme points,arithmetic mean, and weighted mean properties are investigated.

Given the positive real numbers x and y, let A(x, y), G(x, y), and I(x, y) denote their arithmetic mean, geometric mean, and identric mean, respectively. It is proved that for p ≥ 2, the double inequality αA(x, y) + (1− α)G(x, y) < I(x, y) < βA(x, y) + (1− β)G(x, y) holds true for all positive real numbers x 6= y if and only if α ≤ ( 2 e )p and β ≥ 23 . This result complements a similar one est...

Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.

We prove the Murphy and Cohen’s conjecture that the maximum number of collisions of n + 1 elastic particles moving freely on a line is n(n+1) 2 if no interior particle has mass less than the arithmetic mean of the masses of its immediate neighbors. In fact, we prove the stronger result that, for the same conclusion, the condition no interior particle has mass less than the geometric mean, rathe...