Extension of Karamata inequality for generalized inverse trigonometric functions

被引：0
|
作者：
Baricz, Arpad [1 ]
Pogany, Tibor K. [2 ]
机构：
[1] Babes Bolyai Univ, Dept Econ, Cluj Napoca, Romania
[2] Univ Rijeka, Fac Maritime Studies, Rijeka, Croatia
来源：
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA | 2015年 / 60卷 / 03期
关键词：
Karamata's inequality; Ramanujan's question 294; zero-balanced hyper-geometric functions; generalized inverse trigonometric functions; rational upper bounds;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Discussing Ramanujan's Question 294, Karamata established the inequality log x /x-1 <= 1+3 root x / x + 3 root x, (x > 0, x not equal 1), (*) which is the cornerstone of this paper. We generalize the above inequality transforming into terms of arctan and artanh. Moreover, we expand the established result to the class of generalized inverse p-trigonometric arctanp and to hyperbolic artanh(p) functions.
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页码：379 / 384
页数：6
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