A class of k-log-convex functions and their applications to some special functions

Integral Transforms and Special Functions

Volumn 19, Issue 3, 2008, Pages 195-200

  Qi, Feng ^a,b   Guo, Senlin ^c   Guo, Bai Ni ^b   Chen, Shou Xin ^a  

^a HENAN UNIVERSITY   (China)

^b HENAN POLYTECHNIC UNIVERSITY   (China)

^c UNIVERSITY OF MANITOBA   (Canada)

Author keywords

Application; Complete elliptic integrals; Exponential mean; Extended mean values; Gamma function; Generalization; Identric mean; Inequality; K log concave function; K log convex function; Monotonicity; Riemann's zeta function; Special function

Indexed keywords

EID: 40749136341     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652460701722627     Document Type: Article

References (8)

1. A.Sh. Shabani, Some inequalities for the gamma function, J. Inequal. Pure Appl. Math. 6(2) (2007), Article 49. Available at http: //jipam.vu.edu.au/article.php? sid= 852
2. M. Sellami, K. Brahim, and N. Bettaibi, New inequalities for some special and q-special functions, J. Inequal. Pure Appl. Math. 6(2) (2007), Article 47. Available at http: //jipam.vu.edu.au/article.php?sid=857
3. F. Qi, Logarithmic convexity of extended mean values, Proc. Amer. Math. Soc. 130(6) (2002), pp. 1787-1796.
4. _, The extended mean values: definition, properties, monotonicities, comparison, convexities, generalizations, and applications, Cubo Mat. Educ. 5(3) (2003), pp. 63-90.
5. F. Qi, S. Guo, and Sh.-X. Chen, A new upper bound in the second Kershaw's double inequality andits generalizations, J. Comput. Appl. Math. (2008), in press. Available at http: //dx.doi.org/10.1016/j.cam.2007.07.037
6. F. Qi, S. Guo, and B.-N. Guo, Note, on a class of completely monotonic functions involving the polygamma functions, RGMIA Research Rep. Collect. 10(1) (2007), Article 5. Available at http: / /rgmia.vu.edu.au/ v10nl.html
7. F. Qi, Q. Yang, and W. Li, Two logarithmically completely monotonic functions connected with gamma function, Integral Transforms Spec. Funct. 17(7) (2006), pp. 539-542.
8. F. Qi et al., A function involving gamma function and having logarithmically absolute convexity, Integral Transforms Spec. Funct. 18(11) (2007), pp. 837-843.