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.
Citation: Ling Zhu, Branko Malešević. Optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type[J]. AIMS Mathematics, 2021, 6(12): 13024-13040. doi: 10.3934/math.2021753
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.
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Ling Zhu, Branko Malešević. Optimal bounds for the sine and hyperbolic tangent means by arithmetic and centroidal means in exponential type[J]. AIMS Mathematics, 2021, 6(12): 13024-13040. doi: 10.3934/math.2021753
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