α(x)-MONOTONIC FUNCTIONS AND THEIR INEQUALITIES

被引：0

作者：

Pecaric, Josip ^{[1
]}

Smoljak, Ksenija ^{[1
]}

机构：

[1] Univ Zagreb, Fac Text Technol, Zagreb 10000, Croatia

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2011年 / 5卷 / 03期

关键词：

differential equation; a(x)-monotonic function; a(x)-monotonic inequality; exponential convexity; mean value theorems; Stolarsky means;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper a(x)-monotonic functions are defined and some inequalities for them are derived. Related analogous of the Lagrange and the Cauchy mean value theorems are also derived and means of the Cauchy type are generated. Furthermore, it is shown that the monotonicity of the Stolarsky means can be proved using the notion of generalized monotonic functions.

引用

页码：435 / 450

页数：16

共 13 条

[1] Akhiezer N. I., 1965, CLASSICAL MOMENT PRO
[2] [Anonymous], CONVEX FUNCTIONS THE
[3] [Anonymous], 1967, INEQUALITIES
[4] Beckenbach E. F., 1961, Inequalities
[5] Bernstein S, 1929, ACTA MATH-DJURSHOLM, V52, P1
[6] Jaksetic J, 2010, MATH INEQUAL APPL, V13, P899
[7] MITRINOVIC DS, 1991, BOLL UNIONE MAT ITAL, V5B, P407
[8] INEQUALITIES FOR DIFFERENCES OF POWERS
PALES, Z
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 131 (01) : 271 - 281
[9] Pecaric J., 1992, Mathematics in Science and Engineering
[10] PECARIC J., J INEQUAL APPL, V2008

← 1 2 →