Inequalities for the weighted mean of $r$-convex functions
HTML articles powered by AMS MathViewer
- by Mingbao Sun and Xiaoping Yang PDF
- Proc. Amer. Math. Soc. 133 (2005), 1639-1646 Request permission
Abstract:
In this paper, the inequalities for the weighted mean of $r$-convex functions are established. As applications, inequalities between the two-parameter mean of an $r$-convex function and extended mean values are given.References
- Lawrence C. Evans and Ronald F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. MR 1158660
- P. M. Gill, C. E. M. Pearce, and J. Pečarić, Hadamard’s inequality for $r$-convex functions, J. Math. Anal. Appl. 215 (1997), no. 2, 461–470. MR 1490762, DOI 10.1006/jmaa.1997.5645
- Ji Chang Kuang, Changyong budengshi, 2nd ed., Hunan Jiaoyu Chubanshe, Changsha, 1993 (Chinese, with English summary). With a preface by Shan Zhen Lu. MR 1305610
- D. S. Mitrinović, Analytic inequalities, Die Grundlehren der mathematischen Wissenschaften, Band 165, Springer-Verlag, New York-Berlin, 1970. In cooperation with P. M. Vasić. MR 0274686
- C. E. M. Pearce and J. Pečarić, A continuous analogue and an extension of Radó’s formulæ, Bull. Austral. Math. Soc. 53 (1996), no. 2, 229–233. MR 1381764, DOI 10.1017/S0004972700016944
- C. E. M. Pearce, J. Pečarić, and V. Šimić, Stolarsky means and Hadamard’s inequality, J. Math. Anal. Appl. 220 (1998), no. 1, 99–109. MR 1612079, DOI 10.1006/jmaa.1997.5822
- Feng Qi, Generalized weighted mean values with two parameters, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998), no. 1978, 2723–2732. MR 1650779, DOI 10.1098/rspa.1998.0277
- Ming Bao Sun, Inequalities for two-parameter means of convex functions, Math. Practice Theory 27 (1997), no. 3, 193–198 (Chinese, with English and Chinese summaries). MR 1484124
- Kenneth B. Stolarsky, Generalizations of the logarithmic mean, Math. Mag. 48 (1975), 87–92. MR 357718, DOI 10.2307/2689825
- Béla Uhrin, Some remarks about the convolution of unimodal functions, Ann. Probab. 12 (1984), no. 2, 640–645. MR 735860
Additional Information
- Mingbao Sun
- Affiliation: Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China – and – Department of Applied Mathematics, Hunan Institute of Science and Technology, Yueyang 414000, Hunan, People’s Republic of China
- Email: sun_mingbao@163.com
- Xiaoping Yang
- Affiliation: Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094, People’s Republic of China
- Received by editor(s): March 27, 2003
- Published electronically: January 25, 2005
- Additional Notes: This research was supported in part by SF for Pure Research of Natural Sciences of the Education Department of Hunan Province (no.2000C315), and NNSF (no.10271071) of China.
- Communicated by: Carmen C. Chicone
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1639-1646
- MSC (2000): Primary 26D15, 26A51
- DOI: https://doi.org/10.1090/S0002-9939-05-07835-4
- MathSciNet review: 2120261