A double inequality for an integral mean in terms of the exponential and logarithmic means

DOI10.1007/s10998-016-0181-9zbMath1413.26061OpenAlexW2551448546WikidataQ115603590 ScholiaQ115603590MaRDI QIDQ1705218

Feng Qi, Zhen-Hang Yang, Xiao-Ting Shi, Fang-Fang Liu

Publication date: 14 March 2018

Published in: Periodica Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10998-016-0181-9

zbMATH Keywords

modified Bessel function of the first kindlogarithmic meanexponential mean

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Means (26E60) Inequalities involving other types of functions (26D07) Elliptic integrals as hypergeometric functions (33C75)

Related Items (10)

Sharp bounds for the Sándor-Yang means in terms of arithmetic and contra-harmonic means ⋮ Monotonicity and inequalities related to complete elliptic integrals of the second kind ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ On new sharp bounds for the Toader-Qi mean involved in the modified Bessel functions of the first kind ⋮ Special values of the Bell polynomials of the second kind for some sequences and functions ⋮ Lévy-Khintchine representation of Toader-Qi mean ⋮ A sharp lower bound for Toader-Qi mean with applications ⋮ A new chain of inequalities involving the Toader-Qi, logarithmic and exponential means ⋮ On approximating the quasi-arithmetic mean ⋮ Convexity and monotonicity for elliptic integrals of the first kind and applications

Uses Software

• DLMF

Cites Work

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• Optimal combinations bounds of root-square and arithmetic means for Toader mean
• Some inequalities for bounding Toader mean
• New inequalities for hyperbolic functions and their applications
• Inequalities between arithmetic-geometric, Gini, and Toader means
• Refinements, generalizations, and applications of Jordan's inequality and related problems
• Some mean values related to the arithmetic-geometric mean
• Optimal Lehmer mean bounds for the Toader mean
• A double inequality for bounding Toader mean by the centroidal mean
• Sharp bounds for Toader-Qi mean in terms of logarithmic and identric means
• SOME INEQUALITIES AND ABSOLUTE MONOTONICITY FOR MODIFIED BESSEL FUNCTIONS OF THE FIRST KIND
• Optimal bounds for Toader mean in terms of arithmetic and contraharmonic means
• The best bounds for Toader mean in terms of the centroidal and arithmetic means
• Some bounds for the complete elliptic integrals of the first and second kinds
• Some new inequalities for means in two variables
• Some inequalities constructed by Tchebysheff's integral inequality
• A double inequality for the combination of Toader mean and the arithmetic mean in terms of the contraharmonic mean
• Sharp bounds for Toader mean in terms of contraharmonic mean with applications
• An alternative and united proof of a double inequality for bounding the arithmetic-geometric mean
• A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function
• Some inequalities for complete elliptic integrals
• What is the Laplace Transform?
• On approximating the modified Bessel function of the first kind and Toader-Qi mean

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