Refinements of bounds for the arithmetic mean by new Seiffert-like means

Abstract

In the article, we present the sharp upper and lower bounds for the arithmetic mean in terms of new Seiffert-like means, which give some refinements of the results obtained in [1]. As applications, two new inequalities for the sine and hyperbolic sine functions will be established.

Keywords

• seiffert-like mean
• tangent mean
• hyperbolic sine mean
• sine mean
• hyperbolic tangent mean
• arithmetic mean