Ying-Qing Song

Sharp bounds for Seiffert and Neuman-Sándor means in terms of generalized logarithmic means

In this paper, we prove three sharp inequalities as follows: P(a,b)>L2(a,b), T(a,b)>L5(a,b) and M(a,b)>L4(a,b) for all a,b>0 with a≠b. Here, Lr(a,b), M(a,b), P(a,b) and T(a,b) are the r th generalized logarithmic, Neuman-Sándor, first and second Seiffert means of a and b, respectively.MSC:26E60.

Sharp Inequalities for Trigonometric Functions

We establish several sharp inequalities for trigonometric functions and present their corresponding inequalities for bivariate means.

Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean

We give the greatest values , and the least values , in (1/2, 1) such that the double inequalities and hold for any and all with , where , , and are the arithmetic, Neuman-Sandor, contraharmonic, and second Seiffert means of and , respectively.

A Sharp Double Inequality for Trigonometric Functions and Its Applications

We present the best possible parameters and such that the double inequality holds for any . As applications, some new analytic inequalities are established.

Sharp bounds for the arithmetic-geometric mean

In this article, we establish some new inequality chains for the ratio of certain bivariate means, and we present several sharp bounds for the arithmetic-geometric mean.MSC:26E60, 26D07, 33E05.

Sharp Bounds for Toader Mean in terms of Arithmetic and Second Contraharmonic Means

We present the best possible parameters and such that double inequalities , hold for all with , where , and are the arithmetic, second contraharmonic, and Toader means of and , respectively.

Note on certain inequalities for Neuman means

In this paper, we give the explicit formulas for the Neuman means NAH, NHA, NAC, and NCA, and present the best possible upper and lower bounds for these means in terms of the combinations of harmonic mean H, arithmetic mean A, and contraharmonic mean C.MSC:26E60.

Monotonicity of the Ratio of the Power and Second Seiffert Means with Applications

We present the necessary and sufficient condition for the monotonicity of the ratio of the power and second Seiffert means. As applications, we get the sharp upper and lower bounds for the second Seiffert mean in terms of the power mean.

Optimal Lower Generalized Logarithmic Mean Bound for the Seiffert Mean

We present the greatest value such that the inequality holds for all with , where and denote the Seiffert and th generalized logarithmic means of and , respectively.

Sharp Bounds for Neuman Means by Harmonic, Arithmetic, and Contraharmonic Means

We give several sharp bounds for the Neuman means and ( and ) in terms of harmonic mean H (contraharmonic mean C) or the geometric convex combination of arithmetic mean A and harmonic mean H (contraharmonic mean C and arithmetic mean A) and present a new chain of inequalities for certain bivariate means.