Monotonicity and logarithmic concavity of two functions involving exponential function

International Journal of Mathematical Education in Science and Technology

Volumn 39, Issue 5, 2008, Pages 686-691

  Liu, Ai Qi ^a   Li, Guo Fu ^b   Guo, Bai Ni ^c   Qi, Feng ^c  

^a Sanmenxia Polytechnic   (China)

^b ZHENGZHOU NORMAL UNIVERSITY   (China)

^c HENAN POLYTECHNIC UNIVERSITY   (China)

Author keywords

Binet's formula; Exponential function; Inequality; Logarithmic concavity; Monotonicity; Origin

Indexed keywords

EID: 45949104101     PISSN: 0020739X     EISSN: 14645211     Source Type: Journal    
DOI: 10.1080/00207390801986841     Document Type: Article

References (11)

1. P.N. de Souza and J.-N. Silva, Berkeley Problems in Mathematics, 2nd ed., Problem Books in Mathematics, Springer, New York, 2001.
2. J.-Ch. Kuang, Chángyòng Bùděngshì (Applied Inequalities), 3rd ed., Shandong Science and Technology Press, Shandong Province, Jinan City, China, 2004 (Chinese).
3. Y.-D. Wu and Zh.-H. Zhang, The best constant for an inequality, Octogon Math. Mag. 12(1) (2004), pp. 139-141.
4. RGMIA Res. Rep. Coll. 7 (2004), no. 1, Art. 19. Available online at http://rgmia.vu.edu.au/v7n1.html
5. Ch.-P. Chen and F. Qi, Best constant in an inequality connected with exponential functions, Octogon Math. Mag. 12(2) (2004), pp. 736-737.
6. G.E. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge, 1999.
7. H. Alzer and S. Ruscheweyh, A subadditive property of the gamma function, J. Math. Anal. Appl. 285 (2003), pp. 564-577.
8. F. Qi and B.-N. Guo, Subadditive and superadditive properties of the polygamma functions, Math. Inequal. Appl., Vol. 11, p. 2008,
9. RGMIA Res. Rep. Coll. 10 (2007), Suppl., Art. 4. Available at http://rgmia.vu.edu.au/v10(E).html
10. S. Guo and F. Qi, A class of completely monotonic functions related to the remainder of Binet's formula with applications, Tamsui Oxf. J. Math. Sci., 24(2) (2008).
11. F. Qi, A monotonicity result of a function involving the exponential function and an application, RGMIA Res. Rep. Coll. 7(3) (2004), pp. 507-509, Art. 16. Available at http://rgmia.vu.edu.au/v7n3.html