Some papers and preprints in 2007 by Dr. Prof. Feng Qi

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Some papers and preprints in 2007

Twenty one papers formally published in 2007

2007年正式发表的21篇论文

  1. 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 http://dx.doi.org/10.1016/j.cam.2006.09.005.
    • Cited by-被引用情况
      1. 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.
      2. 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.
      3. 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.
      4. Tomislav Burić and Neven Elezović, Some completely monotonic functions related to the psi function, Mathematical Inequalities and Applications 14 (2011), no. 3, 679–691.
      5. 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.
      6. Necdet Batir, On some properties of the gamma function, Expositiones Mathematicae 26 (2008) 187–196; Available online at http://dx.doi.org/10.1016/j.exmath.2007.10.001.
      7. Chao-Ping Chen and Ai-Jun Li, Monotonicity results of integral mean and application to extension of the second Gautschi-Kershaw’s inequality, RGMIA Research Report Collection 10 (2007), no. 4, Article 2; Available online at http://rgmia.org/v10n4.php.
      8. 张小明，石焕南，二个Gautschi型不等式及其应用，不等式研究通讯 14 (2007), no. 2, 179–191.
      9. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  2. Feng Qi, A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums, Australian & New Zealand Industrial and Applied Mathematics Journal 48 (2007), no. 4, 523–532; Available online at http://dx.doi.org/10.1017/S1446181100003199.
    • 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. 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.
      4. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  3. 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.
  4. Feng Qi, Inequalities between the sum of squares and the exponential of sum of a nonnegative sequence, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 3, Article 78; Available online at http://www.emis.de/journals/JIPAM/article895.html.
    • Cited by-被引用情况
      1. Yin Li, On several new Qi’s inequalities, Creative Mathematics and Informatics 20 (2011), no. 1, 90–95.
      2. Gholamreza Zabandan and Majid Mohammadzadeh, Note on an inequality of Qi’s type, Advances and Applications in Mathematical Sciences (2011), in press.
      3. Benharrat Belaïdi, Abdallah El Farissi, and Zinelaâbidine Latreuch, On open problems of F. Qi, Journal of Inequalities in Pure and Applied Mathematics 10 (2009), no. 3, Article 90; Available online at http://www.emis.de/journals/JIPAM/article1146.html.
      4. Huan-Nan Shi, A generalization of Qi’s inequality for sums, Kragujevac Journal of Mathematics 35 (2010), 39–43.
      5. Tamás F. Móri, On an inequality of Feng Qi, Journal of Inequalities in Pure and Applied Mathematics 9 (2008), no. 3, Article 87; Available online at http://www.emis.de/journals/JIPAM/article1024.html.
      6. Huan-Nan Shi, Solution of an open problem proposed by Feng Qi, RGMIA Research Report Collection 10 (2007), no. 4, Article 9; Available online at http://rgmia.org/v10n4.php.
  5. 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 http://dx.doi.org/10.1080/10652460701358976.
    • 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. 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.
      4. 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.
      5. Tomislav Burić and Neven Elezović, Some completely monotonic functions related to the psi function, Mathematical Inequalities and Applications 14 (2011), no. 3, 679–691.
      6. Cristinel Mortici, New sharp inequalities for approximating the factorial function and the digamma function, Miskolc Mathematical Notes 11 (2010), no. 1, 79–86.
      7. Cristinel Mortici, A new Stirling series as continued fraction, Numerical Algorithms 56 (2011), no. 1, 17–26; Available online at http://dx.doi.org/10.1007/s11075-010-9370-4.
      8. Chao-Ping Chen, Monotonicity properties of functions related to the psi function, Applied Mathematics and Computation 217 (2010), 2905–2911; Available online at http://dx.doi.org/10.1016/j.amc.2010.09.013.
  6. Feng Qi and Shou-Xin Chen, Complete monotonicity of the logarithmic mean, Mathematical Inequalities and Applications 10 (2007), no. 4, 799–804.
    • Cited by-被引用情况
      1. 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.
      2. 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.
      3. Ming-Yu Shi, Yu-Ming Chu and Yue-Ping Jiang, Optimal inequalities related to the power, harmonic and identric means, Acta Matematica Scientia Series B (2010), in press.
      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.
  7. Feng Qi, Shou-Xin Chen and Chao-Ping Chen, Monotonicity of ratio between the generalized logarithmic means, Mathematical Inequalities and Applications 10 (2007), no. 3, 559–564.
    • 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. 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.
      3. Bo-Yong Long and Yu-Ming Chu, Optimal inequalities for generalized logarithmic, arithmetic and geometric means, Journal of Inequalities and Applications 2010 (2010), Article ID 806825, 10 pages; Available online at http://dx.doi.org/10.1155/2010/806825.
      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. Alfred Witkowski, Monotonicity and convexity of S-means, Mathematical Inequalities and Applications 13 (2010), no. 1, 33–42.
  8. 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 http://dx.doi.org/10.1080/10652460701318418.
    • 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. 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. 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.
      5. 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.
      6. Chao-Ping Chen, Monotonicity properties of functions related to the psi function, Applied Mathematics and Computation 217 (2010), 2905–2911; Available online at http://dx.doi.org/10.1016/j.amc.2010.09.013.
  9. Feng Qi, Bai-Ni Guo, Senlin Guo and Shou-Xin Chen, A function involving gamma function and having logarithmically absolute convexity, Integral Transforms and Special Functions 18 (2007), no. 11, 837–843; Available online at http://dx.doi.org/10.1080/10652460701528875.
    • 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, Monotonicity properties of functions related to the psi function, Applied Mathematics and Computation 217 (2010), 2905–2911; Available online at http://dx.doi.org/10.1016/j.amc.2010.09.013.
  10. Feng Qi and Senlin Guo, On a new generalization of Martins’ inequality, Journal of Mathematical Inequalities 1 (2007), no. 4, 503–514.
  11. Feng Qi, Da-Wei Niu and Bai-Ni Guo, Monotonic properties of differences for remainders of psi function, International Journal of Pure and Applied Mathematical Sciences 4 (2007), no. 1, 59–66.
  12. Feng Qi and Kit-Wing Yu, Note on an integral inequality, Journal of Mathematical Analysis and Approximation Theory 2 (2007), no. 1, 96–98.
    • Cited by-被引用情况
      1. Bo-Yan Xi, Some generalizations of Feng Qi type integral inequality, private communication.
  13. Wing-Sum Cheung and Feng Qi, Logarithmic convexity of the one-parameter mean values, Taiwanese Journal of Mathematics 11 (2007), no. 1, 231–237; Available online at https://doi.org/10.11650/twjm/1500575060.
    • Cited by-被引用情况
      1. Zhen-Hang Yang, The log-convexity of another class of one-parameter means and its applications, Bulletin of the Korean Mathematical Society 49 (2012), no. 1, 33–47; Available online at http://dx.doi.org/10.4134/BKMS.2012.49.1.033.
      2. 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.
  14. 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 http://dx.doi.org/10.1080/10652460701528933.
  15. Abdolhossein Hoorfar and Feng Qi, Some new bounds for Mathieu’s series, Abstract and Applied Analysis 2007 (2007), Article ID 94854, 10 pages; Available online at http://dx.doi.org/10.1155/2007/94854.
  16. Jian Cao, Da-Wei Niu and Feng Qi, A Wallis type inequality and a double inequality for probability integral, Australian Journal of Mathematical Analysis and Applications 4 (2007), no. 1, Article 3; Available online at http://ajmaa.org/cgi-bin/paper.pl?string=v4n1/V4I1P3.tex.
    • Cited by-被引用情况
      1. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  17. Xiao-Guang Chu, Cheng-En Zhang and Feng Qi, Two new algebraic inequalities with $2n$ variables, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 4, Article 102; Available online at http://www.emis.de/journals/JIPAM/article915.html.
  18. Bai-Ni Guo, Xiao-Ai Li and Feng Qi, Two classes of completely monotonic functions involving gamma and polygamma functions, Australian Journal of Mathematical Analysis and Applications 4 (2007), no. 2, Article 11; Available online at http://ajmaa.org/cgi-bin/paper.pl?string=v4n2/V4I2P11.tex.
  19. Xin Li, Chao-Ping Chen and Feng Qi, Best approximation for constant $e$ and its application, Octogon Mathematical Magazine 15 (2007), no. 1, 23–30.
  20. Xin Li, Chao-Ping Chen and Feng Qi, Monotonicity result for generalized logarithmic means, Tamkang Journal of Mathematics 38 (2007), no. 2, 177–181; Available online at http://dx.doi.org/10.5556/j.tkjm.38.2007.88.
    • Cited by-被引用情况
      1. Bo-Yong Long and Yu-Ming Chu, Optimal inequalities for generalized logarithmic, arithmetic and geometric means, Journal of Inequalities and Applications 2010 (2010), Article ID 806825, 10 pages; Available online at http://dx.doi.org/10.1155/2010/806825.
  21. Zhen-Gang Xiao, Zhi-Hua Zhang and Feng Qi, A type of mean values of several positive numbers with two parameters, Nonlinear Functional Analysis and Applications 12 (2007), no. 4, 687–702.
    • Cited by-被引用情况
      1. Zhen-Gang Xiao, H. M. Srivastava, and Zhi-Hua Zhang, Further refinements of the Jensen inequalities based upon samples with repetitions, Mathematical and Computer Modelling 51 (2010), no. 5-6, 592–600; Available online at http://dx.doi.org/10.1016/j.mcm.2009.11.004.
      2. V. Lokesha, Zhi-Gang Wang, Zhi-Hua Zhang and S. Padmanabhan, The Stolarsky type functions and their monotonicities, Hacettepe Journal of Mathematics and Statistics 38 (2009), no. 2, 119–128.
      3. Ning-Guo Zheng, Zhi-Hua Zhang and Xiao-Ming Zhang, Schur-convexity of two types of one-parameter mean values in $n$ variables, Journal of Inequalities and Applications 2007 (2007), Article ID 78175, 10 pages; Available online at http://dx.doi.org/10.1155/2007/78175.

Seventeen preprints announced in 2007

2007年以预印本形式发表的17篇论文

  1. Feng Qi, A double inequality for divided differences and some identities of psi and polygamma functions, RGMIA Research Report Collection 10 (2007), no. 3, Article 6; Available online at http://rgmia.org/v10n3.php.
  2. Feng Qi, A new lower bound in the second Kershaw’s double inequality, RGMIA Research Report Collection 10 (2007), no. 1, Article 9; Available online at http://rgmia.org/v10n1.php.
    • Cited by-被引用情况
      1. Yuming Chu, Xiaoming Zhang and Xiaomin Tang, An elementary inequality for psi function, Bulletin of the Institute of Mathematics Academia Sinica (New Series) 3 (2008), no. 3, 373–380.
      2. 张小明，褚玉明，解析不等式新论，哈尔滨工业大学出版社，哈尔滨，2009.
      3. 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.
  3. Feng Qi, Complete monotonicity of logarithmic mean, RGMIA Research Report Collection 10 (2007), no. 1, Article 18; Available online at http://rgmia.org/v10n1.php.
  4. Feng Qi, Refinements, extensions and generalizations of the second Kershaw’s double inequality, RGMIA Research Report Collection 10 (2007), no. 2, Article 8; Available online at http://rgmia.org/v10n2.php.
    • Cited by-被引用情况
      1. Yuming Chu, Xiaoming Zhang and Xiaomin Tang, An elementary inequality for psi function, Bulletin of the Institute of Mathematics Academia Sinica (New Series) 3 (2008), no. 3, 373–380.
      2. 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.
      3. Xiaoming Zhang and Yuming Chu, A double inequality for the gamma and psi functions, International Journal of Modern Mathematics 3 (2008), no. 1, 67–73.
      4. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  5. Feng Qi, Jian Cao and Da-Wei Niu, A generalization of van der Corput’s inequality, RGMIA Research Report Collection 10 (2007), Supplement, Article 5; Available online at http://rgmia.org/v10(E).php.
    • Cited by-被引用情况
      1. Xiaoming Zhang and Lokenath Debnath, On a new improvement of van der Corput’s inequality, International Journal of Pure and Applied Mathematics 66 (2011), no. 1, 113–120.
      2. 张小明，褚玉明，解析不等式新论，哈尔滨工业大学出版社，哈尔滨，2009.
  6. 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.
    • Cited by-被引用情况
      1. 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.
      2. Chao-Ping Chen and Ai-Jun Li, Monotonicity results of integral mean and application to extension of the second Gautschi-Kershaw’s inequality, RGMIA Research Report Collection 10 (2007), no. 4, Article 2; Available online at http://rgmia.org/v10n4.php.
      3. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  7. Feng Qi and Bai-Ni Guo, Subadditive and superadditive properties of polygamma functions, RGMIA Research Report Collection 10 (2007), Supplement, Article 4; Available online at http://rgmia.org/v10(E).php.
  8. 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.
    • Cited by-被引用情况
      1. 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.
      2. 张小明，石焕南，二个Gautschi型不等式及其应用，不等式研究通讯 14 (2007), no. 2, 179–191.
      3. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  9. Feng Qi, Bai-Ni Guo and Senlin Guo, A function involving gamma function and having logarithmically absolute convexity, RGMIA Research Report Collection 10 (2007), no. 1, Article 15; Available online at http://rgmia.org/v10n1.php.
  10. Feng Qi and Senlin Guo, New upper bounds in the second Kershaw’s double inequality and its generalizations, RGMIA Research Report Collection 10 (2007), no. 2, Article 1; Available online at http://rgmia.org/v10n2.php.
    • Cited by-被引用情况
      1. Yuming Chu, Xiaoming Zhang and Xiaomin Tang, An elementary inequality for psi function, Bulletin of the Institute of Mathematics Academia Sinica (New Series) 3 (2008), no. 3, 373–380.
      2. 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.
      3. 张小明，褚玉明，解析不等式新论，哈尔滨工业大学出版社，哈尔滨，2009.
      4. Xiaoming Zhang and Yuming Chu, A double inequality for the gamma and psi functions, International Journal of Modern Mathematics 3 (2008), no. 1, 67–73.
      5. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  11. Feng Qi, Senlin Guo and Bai-Ni Guo, A class of $k$-log-convex functions and their applications to some special functions, RGMIA Research Report Collection 10 (2007), no. 1, Article 21; Available online at http://rgmia.org/v10n1.php.
    • Cited by-被引用情况
      1. 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. Feng Qi, Senlin Guo and Bai-Ni Guo, Note on a class of completely monotonic functions involving the polygamma functions, RGMIA Research Report Collection 10 (2007), no. 1, Article 5; Available online at http://rgmia.org/v10n1.php.
    • Cited by-被引用情况
      1. Lingli Wu and Yuming Chu, An inequality for the psi functions, Applied Mathematical Sciences 2 (2008), no. 11, 545–550.
      2. Yuming Chu, Xiaoming Zhang and Xiaomin Tang, An elementary inequality for psi function, Bulletin of the Institute of Mathematics Academia Sinica (New Series) 3 (2008), no. 3, 373–380.
      3. 张小明，褚玉明，解析不等式新论，哈尔滨工业大学出版社，哈尔滨，2009.
      4. Xiaoming Zhang and Yuming Chu, A double inequality for the gamma and psi functions, International Journal of Modern Mathematics 3 (2008), no. 1, 67–73.
      5. Xiao-Ming Zhang, Tie-Quan Xu and Ling-Bo Situ, Geometric convexity of a function involving gamma function and applications to inequality theory, Journal of Inequalities in Pure and Applied Mathematics 8 (2007), no. 1, Article 17; Available online at http://www.emis.de/journals/JIPAM/article830.html.
  13. Feng Qi, Da-Wei Niu and Jian Cao, A general generalization of Jordan’s inequality and a refinement of L. Yang’s inequality, RGMIA Research Report Collection 10 (2007), Supplement, Article 3; Available online at http://rgmia.org/v10(E).php.
    • Cited by-被引用情况
      1. Árpád Baricz and Shanhe Wu, Sharp Jordan-type inequalities for Bessel functions, Publicationes Mathematicae Debrecen 74 (2009), no. 1-2, 107–126.
      2. Ling Zhu, Some new Wilker type inequalities for circular and hyperbolic functions, Abstract and Applied Analysis 2009 (2009), Article ID 485842, 9 pages; Available online at http://dx.doi.org/10.1155/2009/485842.
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