关于第二类s-凸函数的注记
A Note on s2-Convex Functions

作者: 李耀文 :南京大学数学系,江苏 南京 ; 张沂昀 :南京大学大学外语部,江苏 南京 ;

关键词: 凸函数第二类s-凸函数子母定理Milne型不等式Ky-Fan型不等式Convex Functions S-Convex Functions of the Second Type Master Theorem Milne Type Inequalities Ky-Fan Type Inequalities

摘要:
本文中,我们研究了第二类s-凸函数,把凸函数的子母定理推广到s-凸函数的相应形式,由此证明了Ky-Fan型不等式,Milne型不等式。

Abstract: In this paper we study the s-Convex Functions of the second type. We show that a master theorem holds for the s-Convex Functions, and we then apply it to obtain Ky-Fan type inequalities and Milne type inequalities.

文章引用: 李耀文 , 张沂昀 (2016) 关于第二类s-凸函数的注记。 运筹与模糊学, 6, 10-14. doi: 10.12677/ORF.2016.61002

参考文献

[1] Hudzik, H. and Maligranda, L. (1994) Some Remarks on S-Convex Functions. Aequationes Mathematicae, 48, 100- 111.
http://dx.doi.org/10.1007/BF01837981

[2] Dragomir, S.S. and Pearce, C.E.M. (2001) Selected Topics on Hermite-Hadamard Inequalities and Applications. http://rgmir.vu.edu.au/SSDragomirWeb.html

[3] Godunova, E.K. (1967) Convexity of Complex Functions and Its Use in Proving Inequalities (in Russian). Matematicheskie Zametiki, Vol. 1, 495-500. (English Translation: Mathematical Notes, Vol. 1, 326-329).
http://dx.doi.org/10.1007/BF01095554

[4] Woeginger, G.J. (2009) When Cauchy and Holder Met Minkowski: A Tour through Well-Known Inequalities. Mathematics Magazine, 82, 202-207.
http://dx.doi.org/10.4169/193009809X468814

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