Optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type

Abstract

In this paper, optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type are established using the monotone form of L'Hospital's rule and the criterion for the monotonicity of the quotient of power series.

Keywords

• bounds
• seiffert-like means
• sine mean
• hyperbolic tangent mean
• arithmetic mean
• centroidal mean