数学与计算机科学 |
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Toader-Qi平均与其他二元平均的几个确界 |
徐会作1, 钱伟茂2 |
1. 温州广播电视大学 经管学院, 浙江 温州 325000; 2. 湖州广播电视大学 远程教育学院, 浙江 湖州 313000 |
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Some sharp bounds for Toader-Qi mean of other bivariate means |
XU Huizuo1, QIAN Weimao2 |
1. School of Economics and Management, Wenzhou Broadcast and TV University, Wenzhou 325000, Zhejiang Province, China; 2. School of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, Zhejiang Province, China |
[1] TOADER G. Some mean values related to the arithmetic-geometric mean[J]. Journal of Mathematical Analysis and Applications,1998,218(2):358-368. [2] QI F, SHI X T, LIU F F, et al. A double inequality for an integral mean in terms of the exponential and logarithmic means[J]. Periodica Mathematica Hungarica,2016.Doi:10.1007/s10998-016-0181-9. [3] YANG Z H. Some sharp inequalities for the Toader-Qi mean[J]. arXiv:1507.05430. [4] YANG Z H, CHU Y M. On approximating the modified Bessel function of the first kind and Toader-Qi mean[J]. Journal of Inequalities and Applications,2016,2016(1):40. [5] YANG Z H, CHU Y M, SONG Y Q. Sharp bounds for Toader-Qi mean in terms of logarithmic and identic means[J]. Math Inequal Appl,2016,19(2):721-730. [6] YANG Z H, CHU Y M. A sharp lower bound for Toader-Qi mean with applications[J]. Journal of Function Spaces, 2016:Article ID 4165601. file:///D:/Users/Administrator/Downloads/4165601.pdf. [7] GUO B N, QI F. Some inequalities and absolute monotonicity for modified Bessel functions of the first kind[J]. Commun Korean Math Soc,2016,31(2):355-363. [8] ABRAMOWITZ M, STEGUN I A. Handbook of Mathematical Functions:With Formulas, Graphs, and Mathematical Tables[M]. New York:Dover Publications,1965. [9] ANDERSON G D, VAMANAMURTHY M K, VUORINEN M. Conformal Invariants, Quasiconformal Maps, and Special Functions[C]//Quasiconformal Space Mappings. Heidelberg:Springer,1992:1-19. [10] WATSON G N. A Treatise on the Theory of Bessel Functions[M]. Cambridge:Cambridge University Press,1995. [11] SIMI AC'G S, VUORINEN M. Landen inequalities for zero-balanced hypergeometric functions[J]. Abstract and Applied Analysis,2012,2012:932061. [12] THIRUVENKATACHAR V R, NANJUNDIAH T S. Inequalities concerning Bessel functions and orthogonal polynomials[J]. Proceedings Mathematical Sciences,1951,33(6):373-384. |
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