一些凸函數的不等式的研究

On some inequalities for convex functions

林琨諭(Kun-Yu Lin)

指導教授 ： 楊國勝

淡江大學/理學院/數學學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00503

摘要

若f，g：[a,b]→[0,∞) 在 [a,b] 是凸函數，Pachpatte建立了以下的定理：1/(b-a)((∫_a^b)f(x)g(x)dx))≤1/3M(a,b)+1/6N(a,b)其中 M(a,b)=f(a)g(a)+f(b)g(b) 且 N(a,b)=f(a)g(b)+f(b)g(a).本文的主要目的，是要建立一些較此不等式更細緻化的不等式。

關鍵字

厄米阿達碼不等式 ； 凸函數

並列摘要

If f，g：[a,b]→[0,∞) are convex functions on [a,b],Pachpatte proved the following:1/(b-a)((∫_a^b)f(x)g(x)dx))≤1/3M(a,b)+1/6N(a,b),where M(a,b)=f(a)g(a)+f(b)g(b) and N(a,b)=f(a)g(b)+f(b)g(a).We give in this paper several refinements of the above inequality.

並列關鍵字

Hermite-Hadamard inequality ； convex function

參考文獻

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