Some papers and preprints whose titles contain the notions of logarithmically completely functions or logarithmically absolutely monotonic functions

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Some papers and preprints whose titles contain the notions of logarithmically completely functions or logarithmically absolutely monotonic functions

The History

The terminology of the logarithmically completely monotonic function was first used without explicit definition in the paper

R. D. Atanassov and U. V. Tsoukrovski, Some properties of a class of logarithmically completely monotonic functions, Comptes Rendus de l’Académie Bulgare des Sciences 41 (1988), no. 2, 21–23.

The notions of logarithmically completely (absolutely) monotonic functions were first explicitly defined in the following papers and preprints:

  1. Bai-Ni Guo and Feng Qi, A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, University Politehnica of Bucharest Scientific Bulletin Series A—Applied Mathematics and Physics 72 (2010), no. 2, 21–30.
  2. Feng Qi and Chao-Ping Chen, A complete monotonicity property of the gamma function, Journal of Mathematical Analysis and Applications 296 (2004), no. 2, 603–607; available online at https://doi.org/10.1016/j.jmaa.2004.04.026.
  3. Feng Qi and Bai-Ni Guo, A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, arXiv preprint (2009), available online at https://arXiv.org/abs/0903.5038v1.
  4. Feng Qi and Bai-Ni Guo, Complete monotonicities of functions involving the gamma and digamma functions, RGMIA Research Report Collection 7 (2004), no. 1, Article 8, 63–72; available online at http://rgmia.org/v7n1.php.
  5. Feng Qi, Bai-Ni Guo, and Chao-Ping Chen, Some completely monotonic functions involving the gamma and polygamma functions, RGMIA Research Report Collection 7 (2004), no. 1, Article 5, 31–36; available online at http://rgmia.org/v7n1.php.

An important paper on logarithmically completely monotonic functions is

Christian Berg, Integral representation of some functions related to the gamma function, Mediterranean Journal of Mathematics 1 (2004), no. 4, 433–439; available online at https://doi.org/10.1007/s00009-004-0022-6.

Afterwards, these two notations have gradually been becoming standard terminologies in the field of mathematics.

The terminology “logarithmically completely monotone” appears 10+9 times in the monographs

  • René L. Schilling, Renming Song, and Zoran Vondraček, Bernstein Functions: Theory and Applications, Second edition, De Gruyter Studies in Mathematics, 37. Walter de Gruyter & Co., Berlin, 2012; available online at https://doi.org/10.1515/9783110269338.
  • René L. Schilling, Renming Song, and Zoran Vondraček Bernstein Functions: Theory and Applications, De Gruyter Studies in Mathematics, 37, Walter de Gruyter & Co., Berlin, 2010.

BernsteinP67Bernstein2citationsBergBib34Bernstein

Nonself 41 papers and preprints whose titles contain the notions of logarithmically completely functions or logarithmically  absolutely monotonic functions

  1. Vladimir Jovanovic and Milanka Treml, Logarithmically complete monotonicity of reciprocal arctan function, Kragujevac Journal of Mathematics 49 (2025), no. 1, 105–110; available online at https://doi.org/10.46793/KgJMat2501.105J.
  2. Hamed Taghavian, Ross Drummond, and Mikael Johansson, Logarithmically completely monotonic rational functions, Automatica 155 (2023), Paper No. 111122, 11 pages; available online at https://doi.org/10.1016/j.automatica.2023.111122.
  3. Hamed Taghavian, Ross Drummond, and Mikael Johansson, Logarithmically completely monotonic rational functions, arXiv (2023), available online at https://doi.org/10.48550/arXiv.2302.08773.
  4. Khaled Mehrez and Sourav Das, Logarithmically completely monotonic functions related to the $q$-gamma function and its applications, Analysis and Mathematical Physics 12 (2022), no. 2, Paper No. 65, 20 pages; available online at https://doi.org/10.1007/s13324-022-00678-6.
  5. Jing-Feng Tian and Zhenhang Yang, Logarithmically complete monotonicity of ratios of $q$-gamma functions, Journal of Mathematical Analysis and Applications 508 (2022), no. 1, Paper No. 125868, 11 pages; available online at https://doi.org/10.1016/j.jmaa.2021.125868.
  6. O. L. Vinogradov, Logarithmically absolutely monotone trigonometric functions, Journal of Mathematical Sciences 268 (2022), no. 6, 773–782; available online at https://doi.org/10.1007/s10958-022-06217-9.
  7. Vladimir Jovanović and Milanka Treml, Logarithmically complete monotonicity of reciprocal arctan function, arXiv (2021), available online at https://arxiv.org/abs/2112.09960v1.
  8. O. L. Vinogradov, Logarithmically absolutely monotone trigonometric functions, Rossiiskaya Akademiya Nauk. Sankt-Peterburgskoe Otdelenie. Matematicheskii Institut im. V. A. Steklova. Zapiski Nauchnykh Seminarov (POMI) 503 (2021), Issledovaniya po Lineinym Operatoram i Teorii Funktsii. 49, 57–71. (Russian)
  9. Mohammad Soueycatt, Abedalbaset Yonsoo, Ahmad Bekdash, and Nabil Khuder Salman, Logarithmically complete monotonicity of a function involving the gamma functions, American Journal of Applied Mathematics 8 (2020), no. 1, 17–21; available online at https://doi.org/10.11648/j.ajam.20200801.13.
  10. Jamel El Kamel and Khaled Mehrez, A function class of strictly positive definite and logarithmically completely monotonic functions related to the modified Bessel functions, Positivity 22 (2018), no. 5, 1403–1417; Available online at https://doi.org/10.1007/s11117-018-0584-3.
  11. Khaled Mehrez, Logarithmically completely monotonic functions related the $q$-gamma and the $q$-digamma functions with applications, Electronic Journal of Mathematical Analysis  and Applications 6 (2018), no. 1, 174–182.
  12. Kwara Nantomah and Li Yin, Logarithmically complete monotonicity of certain ratios involving the $k$-gamma function, Communications in Mathematics and Applications 9 (2018), no. 4, 559–565; available online at https://doi.org/10.26713/cma.v9i4.1108.
  13. Jumei Zhang, Li Yin, and Honglian You, The logarithmically complete monotonicity and inequalities involving the $k$-gamma function, Bulletin of Mathematics and Statistics Research 6 (2018), no. 3, 70–76.
  14. Khaled Mehrez, A class of logarithmically completely monotonic functions related to the $q$-gamma function and applications, Positivity 21 (2017), no. 1, 495–507; Available online at https://doi.org/10.1007/s11117-016-0431-3.
  15. Bin Chen, Logarithmically complete monotonicity of a class of functions involving the gamma function, Journal of Inner Mongolia Normal University (Nei Mongol Shifan Daxue Xuebao Ziran Kexue Hanwen Ban) 45 (2016), no. 3, 319–321 and 326. (Chinese)
  16. Khaled Mehrez, A class of logarithmically completely monotonic functions relating the $q$-gamma function and applications, arXiv preprint (2015), available online at https://arxiv.org/abs/1512.08548.
  17. Khaled Mehrez, Logarithmically completely monotontic functions related the $q$-gamma and the $q$-digamma functions with applications, arXiv preprint (2015), available online at https://arxiv.org/abs/1511.07156.
  18. Senlin Guo, A class of logarithmically completely monotonic functions and their applications, Journal of Applied Mathematics 2014, Article ID 757462, 5 pages; Available online at https://doi.org/10.1155/2014/757462.
  19. Senlin Guo, H. M. Srivastava, and Wing-Sum Cheung, Some properties of functions related to certain classes of completely monotonic functions and logarithmically completely monotonic functions, Filomat 28 (2014), no. 4, 821–828; Available online at https://doi.org/10.2298/FIL1404821G.
  20. Valmir Krasniqi and Armend Sh. Shabani, On a conjecture of a logarithmically completely monotonic function, The Australian Journal of Mathematical Analysis and Applications 11 (2014), no. 1, Article 5, 5 pages.
  21. Senlin Guo, Logarithmically completely monotonic functions and applications, Applied Mathematics and Computation 221 (2013), 169–176; Available online at https://doi.org/10.1016/j.amc.2013.06.037.
  22. Senlin Guo and Jian-Guo Xu, A strongly logarithmically completely monotonic function and a strongly completely monotonic function with an application, International Conference on Computer Science and Mathematics, Physical Education, and Management, Wuhan, China, 2012.
  23. Valmir Krasniqi, Logarithmically completely monotonic functions involving $p$-gamma functions, Acta Universitatis Apulensis Mathematics Informatics, No. 27 (2011), 253–256.
  24. Yu-Pei Lv, Tian-Chuan Sun, and Yu-Ming Chu, Necessary and sufficient conditions for a class of functions and their reciprocals to be logarithmically completely monotonic, Journal of Inequalities and Applications 2011, Paper No. 36, 8 pages; Available online at https://doi.org/10.1186/1029-242X-2011-36.
  25. Tie-Hong Zhao, Yu-Ming Chu, and Hua Wang, Logarithmically complete monotonicity properties relating to the gamma function, Abstract and Applied Analysis 2011, Article ID 896483, 13 pages; Availble online at https://doi.org/10.1155/2011/896483.
  26. Chaoping Chen, Gang Wang, and Hua Zhu, Two classes of logarithmically completely monotonic functions associated with the gamma functions, 9th International FLINS Conference on Computational Intelligence: Foundations and Applications: Emei, People’s Republich of China: August 2–4, 2010. Computational Intelligence: Foundations and Applications: Proceedings of the 9th International FLINS Conference. World Scientific Proceedings Series on Computer Engineering and Information Science, Volume 4, pages 168-+, 2010; available online at https://doi.org/10.1142/9789814324700_0024.
  27. Valmir Krasniqi and Senlin Guo, Logarithmically completely monotonic functions involving generalized gamma and $q$-gamma functions, Journal of Inequalities and Special Functions 1 (2010), no. 2, 8–16.
  28. Valmir Krasniqi and Faton Merovci, Logarithmically completely monotonic functions involving the generalized gamma function, Le Matematiche (Catania) 65 (2010), no. 2, 15–23; available online at https://doi.org/10.4418/2010.65.2.2.
  29. K. Nonlaopon and R. Kotnara, Some classes of logarithmically completely monotonic functions related to the gamma function, International Journal of Pure and Applied Mathematics 64 (2010), no. 3, 331–338.
  30. K. Nonlaopon and R. Kotnara, Some classes of logarithmically completely monotonic functions related to the gamma function, International Journal of Pure and Applied Mathematics 63 (2010), no. 4, 471–478.
  31. József Sándor, A note on logarithmically completely monotonic ratios of certain mean values, Acta Universitatis Sapientiae Mathematica 2 (2010), no. 1, 84–91.
  32. Tie-Hong Zhao and Yu-Ming Chu, A class of logarithmically completely monotonic functions associated with a gamma function, Journal of Inequalities and Applications 2010, Article ID 392431, 11 pages; Available online at https://doi.org/10.1155/2010/392431.
  33. Miao-Qing An, Logarithmically complete monotonicity and logarithmically absolute monotonicity properties for the gamma function, Communications in Mathematical Analysis 6 (2009), no. 2, 69–78.
  34. Senlin Guo and H. M. Srivastava, A certain function class related to the class of logarithmically completely monotonic functions, Mathematical and Computer Modelling 49 (2009), no. 9-10, 2073–2079; Available online at https://doi.org/10.1016/j.mcm.2009.01.002.
  35. Senlin Guo and H. M. Srivastava, A class of logarithmically completely monotonic functions, Applied Mathematics Letters 21 (2008), no. 11, 1134–1141; Available online at https://doi.org/10.1016/j.aml.2007.10.028.
  36. Chao-Ping Chen, Complete monotonicity and logarithmically complete monotonicity properties for the gamma and psi functions, Journal of Mathematical Analysis and Applications 336 (2007), no. 2, 812–822; Available online at https://doi.org/10.1016/j.jmaa.2007.03.028.
  37. Ai-Jun Li and Chao-Ping Chen, Logarithmically complete monotonicity properties and characterizations of the gamma function, Tamkang Journal of Mathematics 38 (2007), no. 4, 313–322; available online at https://doi.org/10.5556/j.tkjm.38.2007.65.
  38. Jian-She Sun and Zong-Qing Guo, A note on logarithmically completely monotonic functions involving the gamma functions, Communications in Mathematical Analysis 2 (2007), no. 2, 12–16.
  39. Yue-Jin Wei, Su-Ling Zhang, and Chao-Ping Chen, Logarithmically completely monotonic functions and Gurland’s ratio for the gamma functions, Advanced Studies in Contemporary Mathematics (Kyungshang) 15 (2007), no. 2, 253–257.
  40. Ai-Jun Li, Wei-Zhen Zhao, and Chao-Ping Chen, Logarithmically complete monotonicity and Shur-convexity for some ratios of gamma functions, Univerzitet u Beogradu Publikacije Elektrotehničkog Fakulteta Serija Matematika 17 (2006), 88–92; Available online at https://doi.org/10.2298/PETF0617088A.
  41. Ai-Jun Li, Wei-Zhen Zhao, and Chao-Ping Chen, Logarithmically complete monotonicity properties for the ratio of gamma function, Advanced Studies in Contemporary Mathematics (Kyungshang) 13 (2006), no. 2, 183–191.

My own 63 papers and preprints whose titles contain the notions of logarithmically completely (absolutely) monotonic functions

  1. Feng Qi, A logarithmically completely monotonic function and several inequalities for $q$-multinominal coefficients and $q$-multivariate beta functions, Mathematical Inequalities & Applications 27 (2024), no. 1, 115–126; available online at https://doi.org/10.7153/mia-2024-27-08.
  2. Frederic Ouimet and Feng Qi, Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution, Mathematical Inequalities & Applications 25 (2022), no. 3, 703–714; available online at https://doi.org/10.7153/mia-2022-25-45.
  3. Frederic Ouimet and Feng Qi, Logarithmic complete monotonicity of a matrix-parametrized analogue of the multinomial distribution, arXiv preprint (2022), available online at https://arxiv.org/abs/2105.01494v3.
  4. Feng Qi and Bai-Ni Guo, From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions, Journal of Mathematical Analysis and Applications 493 (2021), no. 1, Paper No. 124478, 19 pages; available online at https://doi.org/10.1016/j.jmaa.2020.124478.
  5. Frederic Ouimet and Feng Qi, Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution, arXiv preprint (2021), available online at https://arxiv.org/abs/2105.01494v2.
  6. Frederic Ouimet and Feng Qi, Logarithmically complete monotonicity of a matrix-parametrized analogue of the multinomial distribution, arXiv preprint (2021), available online at https://arxiv.org/abs/2105.01494v1.
  7. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions, Applicable Analysis and Discrete Mathematics 14 (2020), no. 2, 512–527; available online at https://doi.org/10.2298/AADM191111033Q.
  8. Feng Qi and Bai-Ni Guo, From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions, arXiv preprint (2020), available online at https://arxiv.org/abs/2001.02175v1.
  9. Feng Qi, A logarithmically completely monotonic function involving the $q$-gamma function, HAL preprint (2018), available online at https://hal.archives-ouvertes.fr/hal-01803352v1.
  10. Feng Qi, Da-Wei Niu, Dongkyu Lim, and Bai-Ni Guo, Some logarithmically completely monotonic functions and inequalities for multinomial coefficients and multivariate beta functions, HAL preprint (2018), available online at https://hal.archives-ouvertes.fr/hal-01769288v1.
  11. Bai-Ni Guo and Feng Qi, Some inequalities and absolute monotonicity for modified Bessel functions of the first kind, Communications of the Korean Mathematical Society 31 (2016), no. 2, 355–363; available online at https://doi.org/10.4134/CKMS.2016.31.2.355.
  12. Feng Qi and Bai-Ni Guo, Logarithmically complete monotonicity of a function related to the Catalan–Qi function, Acta Universitatis Sapientiae Mathematica 8 (2016), no. 1, 93–102; available online at https://doi.org/10.1515/ausm-2016-0006.
  13. Feng Qi and Bai-Ni Guo, Logarithmically complete monotonicity of Catalan–Qi function related to Catalan numbers, Cogent Mathematics 3 (2016), Article 1179379, 6 pages; available online at https://doi.org/10.1080/23311835.2016.1179379.
  14. Bai-Ni Guo and Feng Qi, Some inequalities and absolute monotonicity for modified Bessel functions of the first kind, ResearchGate Preprint (2015), available online at https://doi.org/10.13140/RG.2.1.3740.1129.
  15. Feng Qi and Wen-Hui Li, A logarithmically completely monotonic function involving the ratio of gamma functions, Journal of Applied Analysis and Computation 5 (2015), no. 4, 626–634; available online at https://doi.org/10.11948/2015049.
  16. Bai-Ni Guo and Feng Qi, Logarithmically complete monotonicity of a power-exponential function involving the logarithmic and psi functions, Global Journal of Mathematical Analysis 3 (2015), no. 2, 77–80; available online at https://doi.org/10.14419/gjma.v3i2.4605.
  17. Fang-Fang Liu, Xiao-Ting Shi, and Feng Qi, A logarithmically completely monotonic function involving the gamma function and originating from the Catalan numbers and function, Global Journal of Mathematical Analysis 3 (2015), no. 4, 140–144; available online at https://doi.org/10.14419/gjma.v3i4.5187.
  18. Feng Qi, A logarithmically completely monotonic function involving the gamma function and originating from the Catalan numbers, ResearchGate Preprint (2015), available online at https://doi.org/10.13140/RG.2.1.1401.2009.
  19. Feng Qi, Logarithmically complete monotonicity of a function related to the Catalan–Qi function, ResearchGate Preprint (2015), available online at https://doi.org/10.13140/RG.2.1.4324.1445.
  20. Feng Qi and Wen-Hui Li, A logarithmically completely monotonic function involving the ratio of gamma functions, arXiv preprint (2015), available online at https://arxiv.org/abs/1303.1877v2.
  21. Feng Qi, Absolute monotonicity of a function involving the exponential function, Global Journal of Mathematical Analysis 2 (2014), no. 3, 184–203; available online at https://doi.org/10.14419/gjma.v2i3.3062.
  22. Feng Qi and Miao-Miao Zheng, Absolute monotonicity of functions related to estimates of first eigenvalue of Laplace operator on Riemannian manifolds, International Journal of Analysis and Applications 6 (2014), no. 2, 123–131.
  23. Feng Qi and Wen-Hui Li, A logarithmically completely monotonic function involving the ratio of two gamma functions and originating from the coding gain, arXiv preprint (2013), available online at https://arXiv.org/abs/1303.1877v1.
  24. Feng Qi and Qiu-Ming Luo, Bounds for the ratio of two gamma functions—From Wendel’s and related inequalities to logarithmically completely monotonic functions, Banach Journal of Mathematical Analysis 6 (2012), no. 2, 132–158; available online at https://doi.org/10.15352/bjma/1342210165.
  25. Senlin Guo, Feng Qi, and H. M. Srivastava, A class of logarithmically completely monotonic functions related to the gamma function with applications, Integral Transforms and Special Functions 23 (2012), no. 8, 557–566; available online at https://doi.org/10.1080/10652469.2011.611331.
  26. Feng Qi and Bai-Ni Guo, A logarithmically completely monotonic function involving the gamma function, Taiwanese Journal of Mathematics 14 (2010), no. 4, 1623–1628; available online at https://doi.org/10.11650/twjm/1500405972.
  27. Feng Qi and Bai-Ni Guo, Some logarithmically completely monotonic functions related to the gamma function, Journal of the Korean Mathematical Society 47 (2010), no. 6, 1283–1297; available online at https://doi.org/10.4134/JKMS.2010.47.6.1283.
  28. Bai-Ni Guo and Feng Qi, A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, University Politehnica of Bucharest Scientific Bulletin Series A—Applied Mathematics and Physics 72 (2010), no. 2, 21–30.
  29. Feng Qi, A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, Journal of Computational and Applied Mathematics 224 (2009), no. 2, 538–543; available online at https://doi.org/10.1016/j.cam.2008.05.030.
  30. Senlin Guo and Feng Qi, A class of logarithmically completely monotonic functions associated with the gamma function, Journal of Computational and Applied Mathematics 224 (2009), no. 1, 127–132; available online at https://doi.org/10.1016/j.cam.2008.04.028.
  31. Feng Qi, Bounds for the ratio of two gamma functions—From Wendel’s and related inequalities to logarithmically completely monotonic functions, arXiv preprint (2009), available online at https://arXiv.org/abs/0904.1048v1.
  32. Feng Qi and Bai-Ni Guo, A property of logarithmically absolutely monotonic functions and the logarithmically complete monotonicity of a power-exponential function, arXiv preprint (2009), available online at https://arXiv.org/abs/0903.5038v1.
  33. Feng Qi and Bai-Ni Guo, Necessary and sufficient conditions for a function involving a ratio of gamma functions to be logarithmically completely monotonic, arXiv preprint (2009), available online at https://arXiv.org/abs/0904.1101v2.
  34. Feng Qi and Bai-Ni Guo, Necessary and sufficient conditions for functions involving a ratio of gamma functions to be logarithmically completely monotonic, arXiv preprint (2009), available online at https://arXiv.org/abs/0904.1101v1.
  35. Feng Qi and Bai-Ni Guo, Some logarithmically completely monotonic functions related to the gamma function, arXiv preprint (2009), available online at https://arXiv.org/abs/0903.5123v1.
  36. Senlin Guo and Feng Qi, More supplements to a class of logarithmically completely monotonic functions associated with the gamma function, arXiv preprint (2009), available online at https://arXiv.org/abs/0904.4027v1.
  37. Feng Qi and Bai-Ni Guo, A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw’s double inequality, Journal of Computational and Applied Mathematics 212 (2008), no. 2, 444–456; available online at https://doi.org/10.1016/j.cam.2006.12.022.
  38. Feng Qi and Bai-Ni Guo, Wendel’s and Gautschi’s inequalities: Refinements, extensions, and a class of logarithmically completely monotonic functions, Applied Mathematics and Computation 205 (2008), no. 1, 281–290; available online at https://doi.org/10.1016/j.amc.2008.07.005.
  39. Feng Qi, Da-Wei Niu, Jian Cao, and Shou-Xin Chen, Four logarithmically completely monotonic functions involving gamma function, Journal of the Korean Mathematical Society 45 (2008), no. 2, 559–573; available online at https://doi.org/10.4134/JKMS.2008.45.2.559.
  40. Senlin Guo and Feng Qi, A logarithmically complete monotonicity property of the gamma function, International Journal of Pure and Applied Mathematics 43 (2008), no. 1, 63–68.
  41. Senlin Guo, Feng Qi, and Hari M. Srivastava, Supplements to a class of logarithmically completely monotonic functions associated with the gamma function, Applied Mathematics and Computation 197 (2008), no. 2, 768–774; available online at https://doi.org/10.1016/j.amc.2007.08.011.
  42. Feng Qi, A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw’s double inequality, Journal of Computational and Applied Mathematics 206 (2007), no. 2, 1007–1014; available online at https://doi.org/10.1016/j.cam.2006.09.005.
  43. Feng Qi, Certain logarithmically $N$-alternating monotonic functions involving gamma and $q$-gamma functions, Nonlinear Functional Analysis and Applications 12 (2007), no. 4, 675–685.
  44. Feng Qi, Three classes of logarithmically completely monotonic functions involving gamma and psi functions, Integral Transforms and Special Functions 18 (2007), no. 7, 503–509; available online at https://doi.org/10.1080/10652460701358976.
  45. Feng Qi, Shou-Xin Chen, and Wing-Sum Cheung, Logarithmically completely monotonic functions concerning gamma and digamma functions, Integral Transforms and Special Functions 18 (2007), no. 6, 435–443; available online at https://doi.org/10.1080/10652460701318418.
  46. Senlin Guo, Feng Qi, and H. M. Srivastava, Necessary and sufficient conditions for two classes of functions to be logarithmically completely monotonic, Integral Transforms and Special Functions 18 (2007), no. 11, 819–826; available online at https://doi.org/10.1080/10652460701528933.
  47. Feng Qi and Bai-Ni Guo, A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw’s double inequality, RGMIA Research Report Collection 10 (2007), no. 2, Article 5; available online at http://rgmia.org/v10n2.php.
  48. Feng Qi and Bai-Ni Guo, Wendel-Gautschi-Kershaw’s inequalities and sufficient and necessary conditions that a class of functions involving ratio of gamma functions are logarithmically completely monotonic, RGMIA Research Report Collection 10 (2007), no. 1, Article 2; available online at http://rgmia.org/v10n1.php.
  49. Feng Qi, Da-Wei Niu, and Jian Cao, Logarithmically completely monotonic functions involving gamma and polygamma functions, Journal of Mathematical Analysis and Approximation Theory 1 (2006), no. 1, 66–74.
  50. Feng Qi, Qiao Yang, and Wei Li, Two logarithmically completely monotonic functions connected with gamma function, Integral Transforms and Special Functions 17 (2006), no. 7, 539–542; available online at https://doi.org/10.1080/10652460500422379.
  51. Chao-Ping Chen and Feng Qi, Logarithmically completely monotonic functions relating to the gamma function, Journal of Mathematical Analysis and Applications 321 (2006), no. 1, 405–411; available online at https://doi.org/10.1016/j.jmaa.2005.08.056.
  52. Chao-Ping Chen, Xin Li, and Feng Qi, A logarithmically completely monotonic function involving the gamma functions, General Mathematics 14 (2006), no. 4, 127–134.
  53. Da-Wei Niu, Jian Cao, and Feng Qi, A class of logarithmically completely monotonic functions related to $(1+1/x)^x$ and an application, General Mathematics 14 (2006), no. 4, 97–112.
  54. Feng Qi, A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality, RGMIA Research Report Collection 9 (2006), no. 4, Article 11; available online at http://rgmia.org/v9n4.php.
  55. Feng Qi, A class of logarithmically completely monotonic functions and the best bounds in the first Kershaw’s double inequality, RGMIA Research Report Collection 9 (2006), no. 2, Article 16, 351–362; available online at http://rgmia.org/v9n2.php.
  56. Feng Qi, Three classes of logarithmically completely monotonic functions involving gamma and psi functions, RGMIA Research Report Collection 9 (2006), Supplement, Article 6; available online at http://rgmia.org/v9(E).php.
  57. Feng Qi, Jian Cao, and Da-Wei Niu, Four logarithmically completely monotonic functions involving gamma function and originating from problems of traffic flow, RGMIA Research Report Collection 9 (2006), no. 3, Article 9; available online at http://rgmia.org/v9n3.php.
  58. Feng Qi, Da-Wei Niu, and Jian Cao, Logarithmically completely monotonic functions involving gamma and polygamma functions, RGMIA Research Report Collection 9 (2006), no. 1, Article 15, 149–157; available online at http://rgmia.org/v9n1.php.
  59. Chao-Ping Chen and Feng Qi, Logarithmically complete monotonicity properties for the gamma functions, Australian Journal of Mathematical Analysis and Applications 2 (2005), no. 2, Article 8; available online at http://ajmaa.org/cgi-bin/paper.pl?string=v2n2/V2I2P8.tex.
  60. Chao-Ping Chen and Feng Qi, Logarithmically completely monotonic ratios of mean values and an application, Global Journal of Mathematics and Mathematical Sciences 1 (2005), no. 1, 71–76.
  61. Feng Qi, Certain logarithmically $N$-alternating monotonic functions involving gamma and $q$-gamma functions, RGMIA Research Report Collection 8 (2005), no. 3, Article 5, 413–422; available online at http://rgmia.org/v8n3.php.
  62. Feng Qi and Wei Li, Two logarithmically completely monotonic functions connected with gamma function, RGMIA Research Report Collection 8 (2005), no. 3, Article 13, 497–493; available online at http://rgmia.org/v8n3.php.
  63. Chao-Ping Chen and Feng Qi, Logarithmically completely monotonic ratios of mean values and an application, RGMIA Research Report Collection 8 (2005), no. 1, Article 18, 147–152; available online at http://rgmia.org/v8n1.php.

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