Some papers and preprints in 2004 by Dr. Prof. Feng Qi

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Some papers and preprints in 2004

Twenty one papers formally published in 2004

2004年正式发表的21篇论文

  1. Feng Qi, An integral expression and some inequalities of Mathieu type series, Rostocker Mathematisches Kolloquium 58 (2004), 37–46.
    • Cited by-被引用情况
      1. Junesang Choi and H. M. Srivastava, Mathieu series and associated sums involving the Zeta functions, Computers & Mathematics with Applications 59 (2010), no. 2, 861–867; Available online at http://dx.doi.org/10.1016/j.camwa.2009.10.008.
      2. Cristinel Mortici, Accurate approximations of the Mathieu series, Mathematical and Computer Modelling 53 (2011), no. 5-6, 909–914; Available online at http://dx.doi.org/10.1016/j.mcm.2010.10.027.
      3. Živorad Tomovski, Some new integral representations of generalized Mathieu series and alternating Mathieu series, Tamkang Journal of Mathematics 41 (2010), no. 4, 303–312.
      4. Tibor K. Pogány and Živorad Tomovski, Bounds improvement for alternating Mathieu type series, Journal of Mathematical Inequalities (2010), in press.
      5. Živorad Tomovski and Delco Leškovski, Refinements and sharpness of some inequalities for Mathieu type series, RGMIA Research Report Collection 11 (2008), Supplement, Article 16; Available online at http://rgmia.org/v11(E).php.
      6. Živorad Tomovski, New integral and series representations of the generalized Mathieu series, Applicable Analysis and Discrete Mathematics 2 (2008), no. 2, 205–212.
      7. Živorad Tomovski and Rudolf Hilfer, Some bounds for alternating Mathieu type series, Journal of Mathematical Inequalities 2 (2008), no. 1, 17–26.
      8. Živorad Tomovski, Integral representations of generalized Mathieu series via Mittag-Leffler type functions, Fractional Calculus and Applied Analysis 10 (2007), no. 2, 1–12.
      9. Tibor K. Pogány and Živorad Tomovski, On Mathieu-type series whose terms contain generalized hypergeometric function ${}_pF_q$ and Meijer’s $G$-function, Mathematical and Computer Modelling 47 (2008), no. 9-10, 952–969.
      10. P. Cerone, Bounding Mathieu type series, RGMIA Research Report Collection 6 (2003), no. 3, Article 7; Available online at http://rgmia.org/v6n3.php.
      11. Tibor K. Pogány and Živorad Tomovski, On multiple generalized Mathieu series, Integral Transforms and Special Functions 17 (2006), no. 4, 285–293.
      12. Tibor K. Pogány, H. M. Srivastava and Živorad Tomovski, Some families of Mathieu $\mathbf{a}$-series and alternating Mathieu $\mathbf{a}$-series, Applied Mathematics and Computation 173 (2006), 69–108.
      13. Tibor K. Pogány, Integral representation of Mathieu $(\mathbf{a,\mathbf{\lambda})$-series, Integral Transforms and Special Functions 16 (2005), no. 8, 685–689.
      14. Biserka Draščić, Tibor K. Pogány, On integral representation of Bessel function of the first kind, Journal of Mathematical Analysis and Applications 308 (2005), no. 2, 775–780.
      15. Biserka Draščić, Tibor K. Pogány, On integral representation of first kind Bessel function, RGMIA Research Report Collection 7 (2004), no. 3, Article 18; Available online at http://rgmia.org/v7n3.php.
      16. H. M. Srivastava and Živorad Tomovski, Some problems and solutions involving Mathieu’s series and its generalizations, Journal of Inequalities in Pure and Applied Mathematics 5 (2004), no. 2, Article 45; Available online at http://www.emis.de/journals/JIPAM/article380.html.
      17. P. Cerone and C. T. Lenard, On integral forms of generalised Mathieu series, Journal of Inequalities in Pure and Applied Mathematics 4 (2003), no. 5, Article 100; Available online at http://www.emis.de/journals/JIPAM/article341.html.
      18. P. Cerone and C. T. Lenard, On integral forms of generalised Mathieu series, RGMIA Research Report Collection 6 (2003), no. 2, Article 19; Available online at http://rgmia.org/v6n2.php.
      19. Tibor K. Pogány, Integral representation of a series which includes the Mathieu $\boldsymbol{a}$-series, Journal of Mathematical Analysis and Applications 296 (2004), no. 1, 309–313.
      20. Tibor K. Pogány, Integral representation of Mathieu $(\boldsymbol{a,\lambda)$-series, RGMIA Research Report Collection 7 (2004), no. 1, Article 9; Available online at http://rgmia.org/v7n1.php.
  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 http://dx.doi.org/10.1016/j.jmaa.2004.04.026.
    • Cited by-被引用情况
      1. Chao-Ping Chen and H. M. Srivastava, Some inequalities and monotonicity properties associated with the gamma and psi functions and the Barnes $G$-function, Integral Transforms and Special Functions 22 (2011), no. 1, 1–15; Available online at http://dx.doi.org/10.1080/10652469.2010.483899.
      2. Chao-Ping Chen, H. M. Srivastava, Li Li, and Seiichi Manyama, Inequalities and monotonicity properties for the psi (or digamma) function and estimates for the Euler-Mascheroni constant, Integral Transforms and Special Functions 22 (2011), no. 9, 681–693; Available online at http://dx.doi.org/10.1080/10652469.2010.538525.
      3. Chao-Ping Chen, Some properties of functions related to the gamma, psi and tetragamma functions, Computers & Mathematics with Applications 62 (2011), no. 9, 3389–3395; Available online at http://dx.doi.org/10.1016/j.camwa.2011.08.053.
      4. 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.
      5. Valmir Krasniqi and Senlin Guo, Logarithmically completely monotonic functions involving generalized gamma and $q$-gamma functions, Journal of Inequalities and Special Functions 1 (2011), no. 2, 8–16.
      6. Tomislav Burić and Neven Elezović, Some completely monotonic functions related to the psi function, Mathematical Inequalities and Applications 14 (2011), no. 3, 679–691.
      7. Yuming Chu, Xiaoming Zhang and Zhihua Zhang, The geometric convexity of a function involving gamma function with applications, Communications of the Korean Mathematical Society 25 (2010), no. 3, 373–383; Available online at http://dx.doi.org/10.4134/CKMS.2010.25.3.373.
      8. Miao-Qing An, A note on an open problem, RGMIA Research Report Collection 12 (2009), no. 2, Article 13; Available online at http://rgmia.org/v12n2.php.
      9. Zhang Xiaohui, Wang Gendi and Chu Yuming, Monotonicity and inequalities for the gamma function, Far East Journal of Mathematical Sciences 21 (2006), no. 1, 33–39.
      10. 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.
      11. 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.
      12. Xiao Li, Monotonicity properties for the gamma and psi functions, Scientia Magna 4 (2008), no. 4, 18–23.
      13. Senlin Guo and H. M. Srivastava, A class of logarithmically completely monotonic functions, Applied Mathematics Letters 21 (2008), no. 11, 1134–1141.
      14. Xin Li and Chao-Ping Chen, Logarithmically completely monotonic functions relating to the gamma functions, Octogon Mathematical Magazine 15 (2007), no. 1, 7–10.
      15. 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. 1, 12–16.
      16. Senlin Guo, On the composition of completely monotonic and related functions, RGMIA Research Report Collection 10 (2007), no. 1, Article 8; Available online at http://rgmia.org/v10n1.php.
      17. Ai-Jun Li, Wei-Zhen Zhao and Chao-Ping Chen, Logarithmically complete monotonicity and Schur-convexity for some ratios of gamma functions, Univerzitet u Beogradu Publikacije Elektrotehničkog Fakulteta, Serija: Matematika 17 (2006), 88–92.
      18. Senlin Guo, Some function classes connected to the class of completely monotonic functions, RGMIA Research Report Collection 9 (2006), no. 2, Article 8, 255–259; Available online at http://rgmia.org/v9n2.php.
  3. Feng Qi and Chao-Ping Chen, Monotonicity and convexity results for functions involving the gamma function, International Journal of Applied Mathematical Sciences 1 (2004), no. 1, 27–36.
    • Cited by-被引用情况
      1. Chao-Ping Chen and H. M. Srivastava, Some inequalities and monotonicity properties associated with the gamma and psi functions and the Barnes $G$-function, Integral Transforms and Special Functions 22 (2011), no. 1, 1–15; Available online at http://dx.doi.org/10.1080/10652469.2010.483899.
      2. Yi-Chao Chen, Toufik Mansour, and Qian Zou, On the complete monotonicity of quotient of gamma functions, Mathematical Inequalities and Applications 15 (2012), in press.
      3. Yuming Chu, Xiaoming Zhang and Zhihua Zhang, The geometric convexity of a function involving gamma function with applications, Communications of the Korean Mathematical Society 25 (2010), no. 3, 373–383; Available online at http://dx.doi.org/10.4134/CKMS.2010.25.3.373.
      4. 张小明，褚玉明，解析不等式新证法，in press.
      5. 张小明，褚玉明，张志华，函数$(\Gamma(x))^{\frac1{x-1}}$的几何凸性及 $\frac{(\Gamma(x+1))^{\frac1x}{(\Gamma(y+1))^{\frac1y}}$的估计, 不等式研究通讯 14 (2007), no. 2, 206–214.
  4. Feng Qi, Bai-Ni Guo and Lokenath Debnath, A lower bound for ratio of power means, International Journal of Mathematics and Mathematical Sciences 2004 (2004), no. 1, 49–53; Available online at http://dx.doi.org/10.1155/S0161171204208158.
    • Cited by-被引用情况
      1. Abramovich, J. Barić, M. Matić and J. Pečarić, On van de Lune-Alzer’s inequality, Journal of Mathematical Inequalities 1 (2007), no. 4, 563–587.
  5. Feng Qi, Qiu-Ming Luo and Bai-Ni Guo, Evaluations of the improper integrals $\int_0^\infty \frac{\sin^{2m}(\alpha x)}{x^{2n}} dx$ and $\int_0^\infty \frac{\sin^{2m+1}(\alpha x)}{x^{2n+1}} dx$, Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics 11 (2004), no. 3, 189–196.
  6. Feng Qi and Nasser Towghi, Inequalities for the ratios of the mean values of functions, Nonlinear Functional Analysis and Applications 9 (2004), no. 1, 15–23.
    • Cited by-被引用情况
      1. Vania Mascioni, A sufficient condition for the integral version of Martins’ inequality, Journal of Inequalities in Pure and Applied Mathematics 5 (2004), no. 2, Article 32; Available online at http://www.emis.de/journals/JIPAM/article382.html.
      2. Jian-She Sun, Monotonicity results and inequalities involving the gamma function, RGMIA Research Report Collection 7 (2004), no. 3, Article 14, 487–494; Available online at http://rgmia.org/v7n3.php.
      3. Jian-She Sun, Sequence inequalities for the logarithmic convex (concave) function, Communications in Mathematical Analysis 1 (2006), no. 1, 6–11.
      4. Jian-She Sun, Sequence inequalities for the logarithmic convex (concave) function, RGMIA Research Report Collection 7 (2004), no. 4, Article 2, 549–554; Available online at http://rgmia.org/v7n4.php.
  7. Chao-Ping Chen and Feng Qi, An alternative proof of monotonicity for the extended mean values, Australian Journal of Mathematical Analysis and Applications 1 (2004), no. 2, Article 11; Available online at http://ajmaa.org/cgi-bin/paper.pl?string=v1n2/V1I2P11.tex.
    • Cited by-被引用情况
      1. Alfred Witkowski, An even easier proof on monotonicity of Stolarsky means, RGMIA Research Report Collection 13 (2010), no. 1, Article 4; Available online at http://rgmia.org/v13n1.php.
      2. Ai-Jun Li, Xue-Min Wang and Chao-Ping Chen, Generalizations of the Ky Fan inequality, Journal of Inequalities in Pure and Applied Mathematics 7 (2006), no. 4, Article 130; Available online at http://www.emis.de/journals/JIPAM/article747.html.
  8. Chao-Ping Chen and Feng Qi, Best constant in an inequality connected with exponential functions, Octogon Mathematical Magazine 12 (2004), no. 2, 736–737.
  9. Chao-Ping Chen and Feng Qi, Generalization of Hardy’s inequality, Proceedings of the Jangjeon Mathematical Society 7 (2004), no. 1, 57–61.
  10. Chao-Ping Chen and Feng Qi, Inequalities of some trigonometric functions, Univerzitet u Beogradu Publikacije Elektrotehničkog Fakulteta, Serija: Matematika 15 (2004), 71–78; Available online at http://dx.doi.org/10.2298/PETF0415071C.
  11. Chao-Ping Chen and Feng Qi, Inequalities relating to the gamma function, Australian Journal of Mathematical Analysis and Applications 1 (2004), no. 1, Article 3; Available online at http://ajmaa.org/cgi-bin/paper.pl?string=v1n1/V1I1P3.tex.
    • Cited by-被引用情况
      1. Tie-Hong Zhao, Yu-Ming Chu, and Hua Wang, Logarithmically complete monotonicity properties relating to the gamma function, Abstract and Applied Analysis 2011 (2011), Article ID 896483, 13 pages; Available online at http://dx.doi.org/10.1155/2011/896483.
      2. 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 (2010), Article ID 392431, 11 pages; Available online at http://dx.doi.org/10.1155/2010/392431.
      3. Xin Li and Chao-Ping Chen, Logarithmically completely monotonic functions relating to the gamma functions, Octogon Mathematical Magazine 15 (2007), no. 1, 7–10.
      4. 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. 1, 12–16.
  12. Chao-Ping Chen and Feng Qi, Monotonicity properties for generalized logarithmic means, Australian Journal of Mathematical Analysis and Applications 1 (2004), no. 2, Article 2; Available online at http://ajmaa.org/cgi-bin/paper.pl?string=v1n2/V1I2P2.tex.
    • Cited by-被引用情况
      1. Yu-Ming Chu and Bo-Yong Long, Best possible inequalities between generalized logarithmic mean and classical means, Abstract and Applied Analysis 2010 (2010), Article ID 303286, 13 pages; Available online at http://dx.doi.org/10.1155/2010/303286.
      2. Wei-Mao Qian and Ning-Guo Zheng, An optimal double inequality for means, Journal of Inequalities and Applications 2010 (2010), Article ID 578310, 11 pages; Available online at http://dx.doi.org/10.1155/2010/578310.
      3. Zhen-Hang Yang, Log-convexity of ratio of the two-parameter symmetric homogeneous functions and an application, Journal of Inequalities and Special Functions 1 (2010), no. 1, 16–29.
      4. Zhen-Hang Yang, Some monotonicity results for the ratio of two-parameter symmetric homogeneous functions, International Journal of Mathematics and Mathematical Sciences 2009 (2009), Article ID 591382, 12 pages; Available online at http://dx.doi.org/10.1155/2009/591382.
      5. László Losonczi, Ratio of Stolarsky means: monotonicity and comparison, Publicationes Mathematicae Debrecen 75 (2009), no. 1-2, 221–238.
      6. Abramovich, J. Barić, M. Matić and J. Pečarić, On van de Lune-Alzer’s inequality, Journal of Mathematical Inequalities 1 (2007), no. 4, 563–587.
      7. Ai-Jun Li, Xue-Min Wang and Chao-Ping Chen, Generalizations of the Ky Fan inequality, Journal of Inequalities in Pure and Applied Mathematics 7 (2006), no. 4, Article 130; Available online at http://www.emis.de/journals/JIPAM/article747.html.
  13. Chao-Ping Chen and Feng Qi, New proofs of monotonicities of generalized weighted mean values, Tamkang Journal of Mathematics 35 (2004), no. 4, 301–304; Available online at http://dx.doi.org/10.5556/j.tkjm.35.2004.188.
  14. Chao-Ping Chen and Feng Qi, Note on a monotonicity property of the gamma function, Octogon Mathematical Magazine 12 (2004), no. 1, 123–125.
  15. Chao-Ping Chen and Feng Qi, On an improper integral, Octogon Mathematical Magazine 12 (2004), no. 2, 710–711.
  16. Chao-Ping Chen and Feng Qi, The best bounds to $\frac{(2n)!}{2^{2n}(n!)^2}$, Mathematical Gazette 88 (2004), 540–542; Available online at http://dx.doi.org/10.1017/S002555720023060X and http://www.jstor.org/stable/3620740.
  17. Chao-Ping Chen, Feng Qi and M. Bencze, On open problem OQ. 1352, Octogon Mathematical Magazine 12 (2004), no. 2, 1049–1050.
  18. Qiu-Ming Luo, Feng Qi and Bai-Ni Guo, K. Petr’s formula of double integral and estimates of its remainder, International Journal of Mathematical Sciences 3 (2004), no. 1, 77–92.
    • Cited by-被引用情况
      1. 雒秋明，安春香，二元函数的Darboux公式和Obreschkoff公式，郑州大学学报（理学版）37 (2005), no. 3, 31–36.
  19. Chao-Ping Chen, Zhi-Qin Wu and Feng Qi, A note on monotonicity for generalized weighted mean values, International Journal of Mathematical Education in Science and Technology 35 (2004), no. 3, 415–418; Available online at http://dx.doi.org/10.1080/00207390310001658410.
  20. Chao-Ping Chen, Jian-Wei Zhao and Feng Qi, Three inequalities involving hyperbolically trigonometric functions, Octogon Mathematical Magazine 12 (2004), no. 2, 592–596.
    • Cited by-被引用情况
      1. Árpád Baricz, Some inequalities involving generalized Bessel functions, Mathematical Inequalities and Applications 10 (2007), no. 4, 827–842.
      2. Árpád Baricz, Redheffer type inequality for Bessel functions, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 11; Available online at http://www.emis.de/journals/JIPAM/article824.html.
  21. Zhong-Pu Ren, Zhi-Qin Wu, Qi-Fa Zhou, Bai-Ni Guo and Feng Qi, Some notes on a functional equation, International Journal of Mathematical Education in Science and Technology 35 (2004), no. 3, 453–456; Available online at http://dx.doi.org/10.1080/00207390410001686599.
    • Cited by-被引用情况
      1. Michael A. B. Deakin, More on a functional equation, International Journal of Mathematical Education in Science and Technology 37 (2006), no. 2, 246–247.

Five preprints announced in 2004

2004年以预印本形式发表的5篇论文

  1. Feng Qi, A monotonicity result of a function involving the exponential function and an application, RGMIA Research Report Collection 7 (2004), no. 3, Article 16, 507–509; Available online at http://rgmia.org/v7n3.php.
  2. Feng Qi and Chao-Ping Chen, A complete monotonicity of the gamma function, RGMIA Research Report Collection 7 (2004), no. 1, Article 1, 3–6; Available online at http://rgmia.org/v7n1.php.
  3. 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.
    • Cited by-被引用情况
      1. Chao-Ping Chen and H. M. Srivastava, Some inequalities and monotonicity properties associated with the gamma and psi functions and the Barnes $G$-function, Integral Transforms and Special Functions 22 (2011), no. 1, 1–15; Available online at http://dx.doi.org/10.1080/10652469.2010.483899.
      2. Chao-Ping Chen, Some properties of functions related to the gamma, psi and tetragamma functions, Computers & Mathematics with Applications 62 (2011), no. 9, 3389–3395; Available online at http://dx.doi.org/10.1016/j.camwa.2011.08.053.
      3. Gabriel Stan, Another extension of van der Corput’s inequality, Bulletin of the Transilvania University of Braşov Series III: Mathematics, Informatics, Physics 3 (2010), no. 52, 133–142.
      4. Peng Gao, Some monotonicity properties of gamma and $q$-gamma functions, ISRN Mathematical Analysis 2011 (2011), Article ID 375715, 15 pages; Available online at http://dx.doi.org/10.5402/2011/375715.
      5. 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.
      6. Tomislav Burić and Neven Elezović, Some completely monotonic functions related to the psi function, Mathematical Inequalities and Applications 14 (2011), no. 3, 679–691.
      7. Miao-Qing An, A note on an open problem, RGMIA Research Report Collection 12 (2009), no. 2, Article 13; Available online at http://rgmia.org/v12n2.php.
      8. Christian Berg, Jorge Mateu and Emilio Porcu, The Dagum family of isotropic correlation functions, Bernoulli 14 (2008), no. 4, 1134–1149.
      9. 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.
      10. Árpád Baricz, Mills’ ratio: Monotonicity patterns and functional inequalities, Journal of Mathematical Analysis and Applications 340 (2008) 1362–1370.
      11. Kenneth S. Berenhaut and Donghui Chen, Inequalities for $3$-log-convex functions, Journal of Inequalities in Pure and Applied Mathematics 9 (2008), no. 4, Article 97; Available online at http://www.emis.de/journals/JIPAM/article1033.html.
      12. Ai-Jun Li and Chao-Ping Chen, Some completely monotonic functions involving the gamma and polygamma functions, Journal of the Korean Mathematical Society 45 (2008), no. 1, 273–287.
      13. Chao-Ping Chen, Two classes of logarithmically completely monotonic functions associated with the gamma function, RGMIA Research Report Collection 10 (2007), no. 4, Article 5; Available online at http://rgmia.org/v10n4.php.
      14. Chao-Ping Chen, Complete monotonicity properties for a ratio of gamma functions, Univerzitet u Beogradu Publikacije Elektrotehničkog Fakulteta, Serija: Matematika 16 (2005), 26–28.
      15. Arcadii Z. Grinshpan and Mourad E. H. Ismail, Completely monotonic functions involving the gamma and $q$-gamma functions, Proceedings of the American Mathematical Society 134 (2006), 1153–1160.
      16. Christian Berg, Integral representation of some functions related to the Gamma function, Mediterranean Journal of Mathematics 1 (2004), no. 4, 433–439.
  4. 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.
    • Cited by-被引用情况
      1. Gabriel Stan, Another extension of van der Corput’s inequality, Bulletin of the Transilvania University of Braşov Series III: Mathematics, Informatics, Physics 3 (2010), no. 52, 133–142.
      2. Peng Gao, Some monotonicity properties of gamma and $q$-gamma functions, ISRN Mathematical Analysis 2011 (2011), Article ID 375715, 15 pages; Available online at http://dx.doi.org/10.5402/2011/375715.
      3. 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.
      4. Christian Berg and Henrik L. Pedersen, A Pick function related to the sequence of volumes of the unit ball in $n$-space, Available online at http://arxiv.org/abs/0912.2185.
      5. Christian Berg, Jorge Mateu and Emilio Porcu, The Dagum family of isotropic correlation functions, Bernoulli 14 (2008), no. 4, 1134–1149.
      6. Arcadii Z. Grinshpan and Mourad E. H. Ismail, Completely monotonic functions involving the gamma and $q$-gamma functions, Proceedings of the American Mathematical Society 134 (2006), 1153–1160.
      7. Christian Berg, Integral representation of some functions related to the Gamma function, Mediterranean Journal of Mathematics 1 (2004), no. 4, 433–439.
  5. Wing-Sum Cheung and Feng Qi, Logarithmic convexity of the one-parameter mean values, RGMIA Research Report Collection 7 (2004), no. 2, Article 15, 331–342; Available online at http://rgmia.org/v7n2.php.
    • Cited by-被引用情况
      1. Zhen-Hang Yang, On the monotonicity and log-convexity for one-parameter homogeneous functions, RGMIA Research Report Collection 8 (2005), no. 2, Article 14; Available online at http://rgmia.org/v8n2.php.

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