1 |
B.-N. Guo and F. Qi, The function ( - )=x : logarithmic convexity and applications to extended mean values, Filomat 25 (2011), no. 4, 63-73. https://doi.org/10.2298/FIL1104063G
DOI
|
2 |
B.-N. Guo, F. Qi, J.-L. Zhao, and Q.-M. Luo, Sharp inequalities for polygamma functions, Math. Slovaca 65 (2015), no. 1, 103-120. https://doi.org/10.1515/ms-2015-0010
DOI
|
3 |
A. Leblanc and B. C. Johnson, On a uniformly integrable family of polynomials defined on the unit interval, JIPAM. J. Inequal. Pure Appl. Math. 8 (2007), no. 3, Article 67, 5 pp.
|
4 |
A.-Q. Liu, G.-F. Li, B.-N. Guo, and F. Qi, Monotonicity and logarithmic concavity of two functions involving exponential function, Internat. J. Math. Ed. Sci. Tech. 39 (2008), no. 5, 686-691. https://doi.org/10.1080/00207390801986841
DOI
|
5 |
D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, New York, 1970.
|
6 |
D. S. Mitrinovic, J. E. Pecaric, and A. M. Fink, Classical and New Inequalities in Analysis, Mathematics and its Applications (East European Series), 61, Kluwer Academic Publishers Group, Dordrecht, 1993. https://doi.org/10.1007/978-94-017-1043-5
|
7 |
F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010; Available online at http://dlmf.nist.gov/.
|
8 |
F. Ouimet, Complete monotonicity of multinomial probabilities and its application to Bernstein estimators on the simplex, J. Math. Anal. Appl. 466 (2018), no. 2, 1609-1617. https://doi.org/10.1016/j.jmaa.2018.06.049
DOI
|
9 |
F. Qi, Limit formulas for ratios between derivatives of the gamma and digamma functions at their singularities, Filomat 27 (2013), no. 4, 601-604. https://doi.org/10.2298/FIL1304601Q
DOI
|
10 |
F. Qi, P. Cerone, S. S. Dragomir, and H. M. Srivastava, Alternative proofs for monotonic and logarithmically convex properties of one-parameter mean values, Appl. Math. Comput. 208 (2009), no. 1, 129-133. https://doi.org/10.1016/j.amc.2008.11.023
DOI
|
11 |
F. Qi and J.-X. Cheng, Some new Steensen pairs, Anal. Math. 29 (2003), no. 3, 219-226. https://doi.org/10.1023/A:1025467221664
DOI
|
12 |
F. Qi and B.-N. Guo, An alternative proof for complete monotonicity of linear combinations of many psi functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01773131.
|
13 |
F. Qi, J.-X. Cheng, and G. Wang, New Steensen pairs, in Inequality theory and applications. Vol. I, 273-279, Nova Sci. Publ., Huntington, NY, 2001.
|
14 |
F. Qi and B.-N. Guo, On Steffensen pairs, J. Math. Anal. Appl. 271 (2002), no. 2, 534-541. https://doi.org/10.1016/S0022-247X(02)00120-8
DOI
|
15 |
F. Qi and B.-N. Guo, Some properties of extended remainder of Binet's first formula for logarithm of gamma function, Math. Slovaca 60 (2010), no. 4, 461-470. https://doi.org/10.2478/s12175-010-0025-7
DOI
|
16 |
F. Qi and B.-N. Guo, The reciprocal of the weighted geometric mean is a Stieltjes function, Bol. Soc. Mat. Mex. (3) 24 (2018), no. 1, 181-202. https://doi.org/10.1007/s40590-016-0151-5
DOI
|
17 |
F. Qi and B.-N. Guo, The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function, Quaest. Math. 41 (2018), no. 5, 653-664. https://doi.org/10.2989/16073606.2017.1396508
DOI
|
18 |
F. Qi and B.-N. Guo, Levy-Khintchine representation of Toader-Qi mean, Math. Inequal. Appl. 21 (2018), no. 2, 421-431. https://doi.org/10.7153/mia-2018-21-29
DOI
|
19 |
F. Qi, B.-N. Guo, and C.-P. Chen, The best bounds in Gautschi-Kershaw inequalities, Math. Inequal. Appl. 9 (2006), no. 3, 427-436. https://doi.org/10.7153/mia-09-41
DOI
|
20 |
M. Abramowitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC, 1964.
|
21 |
H. Alzer and C. Berg, Some classes of completely monotonic functions. II, Ramanujan J. 11 (2006), no. 2, 225-248. https://doi.org/10.1007/s11139-006-6510-5
DOI
|
22 |
W.-S. Cheung and F. Qi, Logarithmic convexity of the one-parameter mean values, Taiwanese J. Math. 11 (2007), no. 1, 231-237. https://doi.org/10.11650/twjm/1500404648
DOI
|
23 |
B.-N. Guo and F. Qi, A simple proof of logarithmic convexity of extended mean values, Numer. Algorithms 52 (2009), no. 1, 89-92. https://doi.org/10.1007/s11075-008-9259-7
DOI
|
24 |
B.-N. Guo and F. Qi, Two new proofs of the complete monotonicity of a function involving the PSI function, Bull. Korean Math. Soc. 47 (2010), no. 1, 103-111. https://doi.org/10.4134/BKMS.2010.47.1.103
DOI
|
25 |
F. Qi, D.-W. Niu, D. Lim, and B.-N. Guo, Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions, HAL archives (2018), available online at https://hal.archives-ouvertes.fr/hal-01769288.
|
26 |
F. Qi and D. Lim, Integral representations of bivariate complex geometric mean and their applications, J. Comput. Appl. Math. 330 (2018), 41-58. https://doi.org/10.1016/j.cam.2017.08.005
DOI
|
27 |
F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between the logarithmic and psi functions, J. Comput. Appl. Math. 361 (2019), 366-371. https://doi.org/10.1016/j.cam.2019.05.001.
DOI
|
28 |
F. Qi, Q.-M. Luo, and B.-N. Guo, The function ( - )=x : ratio's properties, in Analytic number theory, approximation theory, and special functions, 485-494, Springer, New York, 2014. https://doi.org/10.1007/978-1-4939-0258-3_16
|
29 |
R. L. Schilling, R. Song, and Z. Vondracek, Bernstein Functions, second edition, De Gruyter Studies in Mathematics, 37, Walter de Gruyter & Co., Berlin, 2012. https://doi.org/10.1515/9783110269338
|
30 |
D. V. Widder, The Laplace Transform, Princeton Mathematical Series, 6, Princeton University Press, Princeton, NJ, 1941.
|
31 |
S.-Q. Zhang, B.-N. Guo, and F. Qi, A concise proof for properties of three functions involving the exponential function, Appl. Math. E-Notes 9 (2009), 177-183.
|
32 |
F. Qi and W.-H. Li, Integral representations and properties of some functions involving the logarithmic function, Filomat 30 (2016), no. 7, 1659-1674. https://doi.org/10. 2298/FIL1607659Q
DOI
|