ON A TWO-PARAMETER FAMILY OF NONHOMOGENEOUS MEAN VALUES
Keywords:Two-parameter family, nonhomogeneous means, basic property, monotonicity, Tchebycheff integral inequality
In the article, a two-parameter family of nonhomogeneous means is considered and its basic properties and monotonicity are investigated. This paper is dedicated to my advisor, Prof. Yi-Pei Chen, at Ximaen University.
Horst Alzer, "On Stolarsky's mean value family," lnternat. J. Math. Educat. Sci. Tech., 20(1)(1989), 186-189.
E. F. Beckenbach and R. Bellman, Inequalities, Springer-Verlag, Berlin, 1961.
B. C. Carlson, "The logarithmic mean," Amer. Math. Monthly, 79(1972), 615-618.
R. Cisbani, "Contributi alla teoria~elle medie I," Metron, 13(2)(1938), 23-34.
Ji Chen and Hai-bing Shu, "Refinements of Ostile-Terwillinger's inequality," Shuxue Tongxun, (1988), no. 3, 7-8, (in Chinese)
L. Galvani, "Dei limiti a cui tendono alcune media," Boll. Un. Mat. Ital., (6)1927, 173-179
G. H. Hardy, J.E . Littlewood and G. Polya, Inequalities, 2nd Edition, Cambridge University
Press, Cambridge, 1959.
Ji-chang Kuang, Applied Inequalities, 2nd Edition, Hunan Education Press, Changsha, China, 1993, (in Chinese).
E. Leach and M. Sholander, "Extended mean values," Amer. Math. Monthly, 85(1978), 84-90.
E. Leach and M. Sholander. "Extended mean values II," J. Math. Anal. Appl., 92(1983), 207-223.
Tung-Po Lin, "The power mean and the logarithmic mean," Amer. Math. Monthly, 81(1974), 879-883.
D. S. Mitrinovic, Analytic Inequalities, Springer-Verlag, Berlin, 1970.
D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Classical and New Inequalities and Analysis, Kluwer Academic Publishers, Dordrecht, 1993.
Z. Pales, "Inequalities for differences of powers," J. Math. Anal. Appl. 131(1988), 271-281.
G. P6lya and G. Szego, I · soperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, 1951.
Feng QI and Qiu-ming Luo, "Refinements and extensions of an inequality," Mathematics and Informatics Quarterly, 1998 (to appear)
Feng QI and Qiu-ming Luo, "A simple proof of monotonicity for extended means values," J. Math. Anal. Appl., 1998, (to appear).
Feng QI and Shn-lin Xu, "Refinements and extensions of an inequality II," Journal of Mathematical Analysis and Applications, 221(1997), 616-620
Feng QI and Sen-lin Xu, "The function $(b^x-a^x) /x$: Inequalities and properties," Proceedings of American the Mathematical Society, 1998 (to appear).
K. B. Stolarsky, "Generalizations of the logarithmic mean," Math. Mag., 48(1975), 87-92.
Gh. Toader, First Conj. Appl. Math. Mech., Cluj-Napoca, 1988.
Gh. Toader, "A generalization of geometric (or) harmomc means," ' Babes-Bolyai' U niv. Fae. Math. Phys. Res. Sem. Math. Anal. (2)1989, 21-28.
M. D. Tobey, "A two-parameter homogeneous mean value" Proc. Amer. Math. Soc., 18(1967), 9-14.
Ren-er Yang and Dong-ji Cao, "Generalizations of the logarithmic mean," J. Ningbo Univ (2)1989, 105-108.
Feng QI, "Generalized weighted mean values with two parameters," Proceedings of the Royal Society of London A 454(1998), 1-10.
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