Some papers and preprints in 2015 by Dr. Prof. Feng Qi

Some papers and preprints in 2015

Part One: Fifty-two Papers Formally Published in 2015

第一部分：2015年正式发表的52篇论文

1. Feng Qi, Complete monotonicity of functions involving the tri- and tetra-gamma functions, Proceedings of the Jangjeon Mathematical Society 18 (2015), no. 2, 253–264; Available online at http://dx.doi.org/10.17777/pjms.2015.18.2.253.
2. Feng Qi, Complete monotonicity of functions involving the $q$-trigamma and $q$-tetragamma functions, Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas 109 (2015), no. 2, 419–429; Available online at http://dx.doi.org/10.1007/s13398-014-0193-3.
3. Feng Qi, Derivatives of tangent function and tangent numbers, Applied Mathematics and Computation 268 (2015), 844–858; Available online at http://dx.doi.org/10.1016/j.amc.2015.06.123.
4. Feng Qi, Pólya type integral inequalities: origin, variants, proofs, refinements, generalizations, equivalences, and applications, Mathematical Inequalities & Applications 18 (2015), no. 1, 1–38; Available online at http://dx.doi.org/10.7153/mia-18-01.
5. Feng Qi, Properties of modified Bessel functions and completely monotonic degrees of differences between exponential and trigamma functions, Mathematical Inequalities & Applications 18 (2015), no. 2, 493–518; Available online at http://dx.doi.org/10.7153/mia-18-37.
6. Feng Qi, Dmitry Victorovich Dolgy, Taekyun Kim, and Cheon Seoung Ryoo, On the partially degenerate Bernoulli polynomials of the first kind, Global Journal of Pure and Applied Mathematics 11 (2015), no. 4, 2407–2412.
7. Feng Qi and Bai-Ni Guo, Remarks on complete monotonicity of a function involving the gamma function, Problemy Analiza-Issues of Analysis 4 (22) (2015), no. 1, 66–72; Available online at http://dx.doi.org/10.15393/j3.art.2015.2789.
8. Feng Qi, Wei-Dong Jiang, and Jian Cao, Two double inequalities for the Seiffert mean in terms of the arithmetic, centroidal, and contra-harmonic means, Advanced Studies in Contemporary Mathematics (Kyungshang) 25 (2015), no. 4, 547–552.
9. Feng Qi, Dae San Kim, Tae-Kyun Kim, and Dmitry V. Dolgy, Multiple-poly-Bernoulli polynomials of the second kind, Advanced Studies in Contemporary Mathematics (Kyungshang) 25 (2015), no. 1, 1–7.
10. 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 http://dx.doi.org/10.11948/2015049.
11. Feng Qi and Cristinel Mortici, Some best approximation formulas and inequalities for the Wallis ratio, Applied Mathematics and Computation 253 (2015), 363–368; Available online at http://dx.doi.org/10.1016/j.amc.2014.12.039.
12. Feng Qi and Cristinel Mortici, Some inequalities for the trigamma function in terms of the digamma function, Applied Mathematics and Computation 271 (2015), 502–511; Available online at http://dx.doi.org/10.1016/j.amc.2015.09.039.
13. Feng Qi and Xiao-Jing Zhang, An integral representation, some inequalities, and complete monotonicity of the Bernoulli numbers of the second kind, Bulletin of the Korean Mathematical Society 52 (2015), no. 3, 987–998; Available online at http://dx.doi.org/10.4134/BKMS.2015.52.3.987.
14. Feng Qi, Xiao-Jing Zhang, and Wen-Hui Li, An elementary proof of the weighted geometric mean being a Bernstein function, University Politehnica of Bucharest Scientific Bulletin Series A—Applied Mathematics and Physics 77 (2015), no. 1, 35–38.
15. Feng Qi, Tian-Yu Zhang, and Bo-Yan Xi, Hermite–Hadamard-type integral inequalities for functions whose first derivatives are convex, Ukrainian Mathematical Journal 67 (2015), no. 4, 625–640; Available online at http://dx.doi.org/10.1007/s11253-015-1103-3.
16. Feng Qi, Tian-Yu Zhang, and Bo-Yan Xi, Hermite–-Hadamard type integral inequalities for functions whose first derivatives are of convexity, Ukrains’kyi Matematychnyi Zhurnal 67 (2015), no. 4, 555–567; Available online at http://umj.imath.kiev.ua/.
17. Feng Qi and Miao-Miao Zheng, Explicit expressions for a family of the Bell polynomials and applications, Applied Mathematics and Computation 258 (2015), 597–607; Available online at http://dx.doi.org/10.1016/j.amc.2015.02.027.
18. Ling Chun and Feng Qi, Inequalities of Simpson type for functions whose third derivatives are extended $s$-convex functions and applications to means, Journal of Computational Analysis and Applications 19 (2015), no. 3, 555–569.
19. Bai-Ni Guo and Feng Qi, A new explicit formula for the Bernoulli and Genocchi numbers in terms of the Stirling numbers, Global Journal of Mathematical Analysis 3 (2015), no. 1, 33–36; Available online at http://dx.doi.org/10.14419/gjma.v3i1.4168.
20. Bai-Ni Guo and Feng Qi, An explicit formula for Bernoulli numbers in terms of Stirling numbers of the second kind, Journal of Analysis & Number Theory 3 (2015), no. 1, 27–30.
21. 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 http://dx.doi.org/10.14419/gjma.v3i2.4605.
22. Bai-Ni Guo and Feng Qi, On the degree of the weighted geometric mean as a complete Bernstein function, Afrika Matematika 26 (2015), no. 7, 1253–1262; Available online at http://dx.doi.org/10.1007/s13370-014-0279-2.
23. Bai-Ni Guo and Feng Qi, On the increasing monotonicity of a sequence originating from computation of the probability of intersecting between a plane couple and a convex body, Turkish Journal of Analysis and Number Theory 3 (2015), no. 1, 21–23; Available online at http://dx.doi.org/10.12691/tjant-3-1-5.
24. Bai-Ni Guo and Feng Qi, On the Wallis formula, International Journal of Analysis and Applications 8 (2015), no. 1, 30–38.
25. Bai-Ni Guo and Feng Qi, Six proofs for an identity of the Lah numbers, Online Journal of Analytic Combinatorics 10 (2015), 5 pages.
26. Bai-Ni Guo, Feng Qi, and Qiu-Ming Luo, The additivity of polygamma functions, Filomat 29 (2015), no. 5, 1063–1066; Available online at http://dx.doi.org/10.2298/FIL1505063G.
27. Bai-Ni Guo, Feng Qi, Jiao-Lian Zhao, and Qiu-Ming Luo, Sharp inequalities for polygamma functions, Mathematica Slovaca 65 (2015), no. 1, 103–120; Available online at http://dx.doi.org/10.1515/ms-2015-0010.
28. Xu-Yang Guo, Feng Qi, and Bo-Yan Xi, Some new Hermite–Hadamard type inequalities for differentiable co-ordinated convex functions, Cogent Mathematics (2015), 2:1092195, 8 pages; Available online at http://dx.doi.org/10.1080/23311835.2015.1092195.
29. Xu-Yang Guo, Feng Qi, and Bo-Yan Xi, Some new Hermite–Hadamard type inequalities for geometrically quasi-convex functions on co-ordinates, Journal of Nonlinear Sciences and Applications 8 (2015), no. 5, 740–749.
30. Wei-Dong Jiang and Feng Qi, Sharp bounds for Neuman-Sándor mean in terms of the power and contraharmonic means, Cogent Mathematics (2015), 2:995951, 7 pages; Available online at http://dx.doi.org/10.1080/23311835.2014.995951.
31. Cristinel Mortici and Feng Qi, Asymptotic formulas and inequalities for the gamma function in terms of the tri-gamma function, Results in Mathematics 67 (2015), no. 3-4, 395–402; Available online at http://dx.doi.org/10.1007/s00025-015-0439-1.
32. Chun-Fu Wei and Feng Qi, Several closed expressions for the Euler numbers, Journal of Inequalities and Applications 2015, 2015:219, 8 pages; Available online at http://dx.doi.org/10.1186/s13660-015-0738-9.
33. Ying Wu, Feng Qi, and Da-Wei Niu, Integral inequalities of Hermite–Hadamard type for the product of strongly logarithmically convex and other convex functions, Maejo International Journal of Science and Technology 9 (2015), no. 3, 394–402.
34. Bo-Yan Xi and Feng Qi, Inequalities of Hermite-Hadamard type for extended $s$-convex functions and applications to means, Journal of Nonlinear and Convex Analysis 16 (2015), no. 5, 873–890.
35. Bo-Yan Xi and Feng Qi, Integral inequalities of Hermite–Hadamard type for $((\alpha,m), \log)$-convex functions on co-ordinates, Problemy Analiza-Issues of Analysis 4 (22) (2015), no. 2, 73–92; Available online at http://dx.doi.org/10.15393/j3.art.2015.2829.
36. Bo-Yan Xi and Feng Qi, Some new integral inequalities of Hermite–Hadamard type for $(\log, (\alpha,m))$-convex functions on co-ordinates, Studia Universitatis Babeş-Bolyai Mathematica 60 (2015), no. 4, 509–525.
37. Bo-Yan Xi, Feng Qi, and Tian-Yu Zhang, Some inequalities of Hermite–Hadamard type for $m$-harmonic-arithmetically convex functions, ScienceAsia 41 (2015), no. 5, 357–361; Available online at http://dx.doi.org/10.2306/scienceasia1513-1874.2015.41.357.
38. Hong-Ping Yin and Feng Qi, Hermite–Hadamard type inequalities for the product of $(\alpha,m)$-convex functions, Journal of Nonlinear Sciences and Applications 8 (2015), no. 3, 231–236; Available online at https://doi.org/10.22436/jnsa.008.03.07.
39. Hong-Ping Yin and Feng Qi, Hermite-Hadamard type inequalities for the product of $(\alpha,m)$-convex functions, Missouri Journal of Mathematical Sciences 27 (2015), no. 1, 71–79; Available online at http://projecteuclid.org/euclid.mjms/1449161369.
40. Shu-Ping Bai, Jian Sun, and Feng Qi, On inequalities of Hermite-Hadamard type for co-ordinated $(\alpha_1,m_1)$-$(\alpha_2,m_2)$-convex functions, Global Journal of Mathematical Analysis 3 (2015), no. 4, 145–149; Available online at http://dx.doi.org/10.14419/gjma.v3i4.5432.
41. Dmitry V. Dolgy, Taekyun Kim, Feng Qi, and Jong Jin Seo, A note on three variable symmetric identities for modified $q$-Bernoulli polynomials arising from bosonic $p$-adic integral on $\mathbb{Z}_p$, Applied Mathematical Sciences 9 (2015), no. 92, 4575–4582; Available online at http://dx.doi.org/10.12988/ams.2015.5339.
42. Dmitry V. Dolgy, Taekyun Kim, Feng Qi, and Jong Jin Seo, A note on three variable symmetric identities for $q$-Euler polynomials arising from fermionic $p$-adic integral on $\mathbb{Z}_p$, Applied Mathematical Sciences 9 (2015), no. 77, 3819–3826; Available online at http://dx.doi.org/10.12988/ams.2015.53229.
43. Jü Hua, Bo-Yan Xi, and Feng Qi, Some new inequalities of Simpson type for strongly $s$-convex functions, Afrika Matematika 26 (2015), no. 5-6, 741–752; Available online at http://dx.doi.org/10.1007/s13370-014-0242-2.
44. Ai-Ping Ji, Tian-Yu Zhang, and Feng Qi, Integral inequalities of Hermite-Hadamard type for $(\alpha,m)$-GA-convex functions, Journal of Computational Analysis and Applications 18 (2015), no. 2, 255–265.
45. 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 http://dx.doi.org/10.14419/gjma.v3i4.5187.
46. Xiao-Ting Shi, Fang-Fang Liu, and Feng Qi, An integral representation of the Catalan numbers, Global Journal of Mathematical Analysis 3 (2015), no. 3, 130–133; Available online at http://dx.doi.org/10.14419/gjma.v3i3.5055.
47. Lei-Lei Wang, Bo-Yan Xi, and Feng Qi, On $\alpha$-locally doubly diagonally dominant matrices, University Politehnica of Bucharest Scientific Bulletin Series A—Applied Mathematics and Physics 77 (2015), no. 2, 163–172.
48. Shu-Hong Wang, Bo-Yan Xi, and Feng Qi, Some integral inequalities in terms of supremum norms of $n$-time differentiable functions, Mathematical Science Letters 4 (2015), no. 3, 261–267; Available online at http://dx.doi.org/10.12785/msl/040307.
49. Hong-Ping Yin, Huan-Nan Shi, and Feng Qi, On Schur $m$-power convexity for ratios of some means, Journal of Mathematical Inequalities 9 (2015), no. 1, 145–153; Available online at http://dx.doi.org/10.7153/jmi-09-14.
50. Muhammad Aslam Noor, Khalida Inayat Noor, Muhammad Uzair Awan, and Feng Qi, Hermite–Hadamard type inequalities for logarithmically $h$-preinvex functions, Cogent Mathematics (2015), 2:1035856, 9 pages; Available online at http://dx.doi.org/10.1080/23311835.2015.1035856.
51. Jian Sun, Zhi-Ling Sun, Bo-Yan Xi, and Feng Qi, Schur-geometric and Schur-harmonic convexity of an integral mean for convex functions, Turkish Journal of Analysis and Number Theory 3 (2015), no. 3, 87–89; Available online at http://dx.doi.org/10.12691/tjant-3-3-4.
52. 席博彦，祁锋，$s$-对数凸函数的Hermite–Hadamard型不等式，数学物理学报35A (2015), no. 3, 515–524.

Part Two: Thirty-four Preprints Published in 2015

第二部分：2015年以预印本形式发表的34篇论文

1. Feng Qi, A double inequality for ratios of the Bernoulli numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3461.2641.
2. Feng Qi, A logarithmically completely monotonic function involving the gamma function and originating from the Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.1401.2009.
3. Feng Qi, Asymptotic expansions, complete monotonicity, and inequalities of the Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.4371.6321.
4. Feng Qi, Estimates of the Gap of Two Eigenvalues in the Schrödinger Operator and the First Eigenvalue of the Laplace Operator, The thesis supervised by Professor Yi-Pei Chen and submitted in April 1989 for the Master Degree of Science in Mathematics at Xiamen University in China, available online at http://dx.doi.org/10.13140/RG.2.1.2104.0802. (Chinese)
5. Feng Qi, Logarithmically complete monotonicity of a function related to the Catalan-Qi function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.4324.1445.
6. Feng Qi, On sum of the Lah numbers and zeros of the Kummer confluent hypergeometric function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.4089.9683.
7. Feng Qi, Some inequalities for the Bell numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.2544.2721.
8. Feng Qi, Some properties and generalizations of the Catalan, Fuss, and Fuss-Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.1778.3128.
9. Feng Qi, Two closed forms for the Bernoulli polynomials, available online at http://arxiv.org/abs/1506.02137.
10. Feng Qi, Two product representations and several properties of the Fuss-Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.1655.6004.
11. Feng Qi and Bai-Ni Guo, Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/2.1.2733.3928.
12. Feng Qi and Bai-Ni Guo, Remarks on complete monotonicity of a function involving the gamma function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.2378.2249.
13. Feng Qi, Fang-Fang Liu, and Xiao-Ting Shi, Comments on two completely monotonic functions involving the $q$-trigamma function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3267.4401.
14. Feng Qi, Mansour Mahmoud, Xiao-Ting Shi, and Fang-Fang Liu, Some properties of the Catalan-Qi function related to the Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3810.7369.
15. Feng Qi and Cristinel Mortici, Some inequalities for the trigamma function in terms of the digamma function, available online at http://arxiv.org/abs/1503.03020.
16. Feng Qi, Cristinel Mortici, and Bai-Ni Guo, Some properties of a sequence arising from computation of the intersecting probability between a plane couple and a convex body, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.1176.0165.
17. Feng Qi, Xiao-Ting Shi, and Pietro Cerone, A unified generalization of the Catalan, Fuss, Fuss-Catalan numbers and Catalan-Qi function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3198.6000.
18. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, An exponential representation for a function involving the gamma function and originating from the Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.1086.4486.
19. Feng Qi, Xiao-Ting Shi, Mansour Mahmoud, and Fang-Fang Liu, Schur-convexity of the Catalan-Qi function, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.2434.4802.
20. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, An integral representation, complete monotonicity, and inequalities of the Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3754.4806.
21. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, Expansions of the exponential and the logarithm of expansions and applications, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3309.2000.
22. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, Several formulas for special values of the Bell polynomials of the second kind and applications, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3230.1927.
23. Feng Qi, Xiao-Ting Shi, and Fang-Fang Liu, Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.2462.1606.
24. Feng Qi, Xiao-Ting Shi, Fang-Fang Liu, and Zhen-Hang Yang, A double inequality for an integral mean in terms of the exponential and logarithmic means, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.2353.6800.
25. Feng Qi and Chun-Fu Wei, Several closed expressions for the Euler numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/2.1.3474.7688.
26. Bai-Ni Guo and Feng Qi, Explicit formulas for special values of the Bell polynomials of the second kind and the Euler numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/2.1.3794.8808.
27. Bai-Ni Guo and Feng Qi, On inequalities for the exponential and logarithmic functions and means, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.5126.2885.
28. 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 http://dx.doi.org/10.13140/RG.2.1.3740.1129.
29. Dongkyu Lim and Feng Qi, On the Appell type $\lambda$-Changhee polynomials, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3908.8487.
30. Mansour Mahmoud and Feng Qi, Three identities of Catalan-Qi numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.3462.9607.
31. Bo-Yan Xi and Feng Qi, Some integral inequalities of Hermite–Hadamard type for $s$-logarithmically convex functions, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.4385.9044.
32. Xiao-Ting Shi, Fang-Fang Liu, and Feng Qi, An integral representation of the Catalan numbers, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/RG.2.1.2273.6485.
33. Bo-Yan Xi, Shu-Ping Bai, and Feng Qi, Some new inequalities of Hermite-Hadamard type for $(\alpha,m_1)$-$(s,m_2)$-convex functions on co-ordinates, ResearchGate Preprint (2015), available online at http://dx.doi.org/10.13140/2.1.2919.7126.

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1. Several of communicating e-mails with the editors of Missouri Journal of Mathematical Sciences

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