在本文中，我們研究在平面上三角形區域與圓區域或空間中球

體的凸函數，得到一些類似阿達瑪不等式。最後利用凸函數的性質，

推得逆的Holder不等式。

In this paper we study Convex function in the triangle or 

circle or ball , get some similar Hadamard inequality. 

Finally, Finally, the nature of the use of convex push 

inverse the Holder inequality.

1. 前言.............................1

2. 不等式的推廣.....................1

3. 不等式的應用.....................7

4. 參考文獻.........................14

[1] S. S. Dragomir and C. E. M. Pearce, Selected Topics on Hermite-Hadamard Type Inequalities and Applications, RGMIA Monographs, Victoria University, 2000.

[2] S. S. Dragomir, Dragoljub M. Milošević, Jozsef Sador, On some refinements of Hadamard’s inequalities and applications. UNIV. BEOGRAD. PUBL. ELEKTROTEHN.FAK. Ser. Mat. 4(1993),3－10.

[3] S.S. Dragomir. On the Hadamard’s inequality for convex functions on the Co-Ordinates in a Rectangle from the plane. Taiwanese Journal of Mathematics Vol. 5,NO. 4,pp. 775－788.

[4] S.S.Dragomir, Y.J.Cho, and S.S.Kim, Inequalities of Hadamard’s type for   Lipschitzian Mappings and Their Applications. Journal of Mathematical Analysis 
and Applications 245, 489－501(2000)

[5]S.S. Dragomir, Two Mappings in Connection to Hadamard’s inequality Journal of Mathematical Analysis and Applications 167, 49－56 (1992)

[6] J.B. DIAZ and F. T. METCALF: Complementary inequalities I: Inequalities complementary to Cauch’s inequality for sums of real numbers. J. Math. Anal. Appl. 9.59－74 (1964)

[7] T. Furuta, Basic properties of the generalized Kantorovich constant  , Acta Sci. Math 70 (2004) 319–337.

[8] Kuei-Lin Tseng, and Chung-Shin Wang, Some Refinements of the Fejer’s Inequality for Convex Functions. Tamsui Oxford Journal of Mathematical Sciences 21(1) (2005) 95－104.

[9] M.MATIĆ and J. PEČARIĆ, Note inequalities of  Hadamard’s type for Lipschitzian Mappings. Tamkang Jour. Math. Vol.32, No. 2, pp.127－130.

[10] Z. NEHARJ: Inverse Holder inequalities. J. Math. Anal. Appl. 21 405－420 (1968)

[11] W. SPECHT: Zur Theorie der elementaren Mittel. Math. Z. 72, 91-98(1960)