On two new means of two arguments III

In this paper authors establish the two sided inequalities for the following two new means $$X=X(a,b)=Ae^{G/P-1},\quad Y=Y(a,b)=Ge^{L/A-1}.$$ As well as many other well known inequalities involving the identric mean $I$ and the logarithmic mean are refined from the literature as an application.Comment: 14. arXiv admin note: substantial text overlap with arXiv:1509.0197

On some inequalities for the identric, logarithmic and related means

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.Comment:

Logarithmic mean inequality for generalized trigonometric and hyperbolic functions

In this paper we study the convexity and concavity properties of generalized trigonometric and hyperbolic functions in case of Logarithmic mean.Comment: