Convexity properties of generalized trigonometric and hyperbolic functions

被引：15
|
作者：
Baricz, Arpad [1 ]
Bhayo, Barkat Ali [2 ]
Klen, Riku [3 ]
机构：
[1] Univ Babes Bolyai, Dept Econ, Cluj Napoca 400591, Romania
[2] Univ Jyvaskyla, Dept Math Informat Technol, Jyvaskyla 40014, Finland
[3] Univ Turku, Dept Math & Stat, Turku, Finland
来源：
AEQUATIONES MATHEMATICAE | 2015年 / 89卷 / 03期
关键词：
Power mean; eigenfunctions of p-Laplacian; generalized trigonometric functions; generalized inverse trigonometric functions; convexity with respect to power means; geometrical convexity;
D O I：
10.1007/s00010-013-0222-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the power mean inequality for generalized trigonometric and hyperbolic functions with two parameters. The generalized p-trigonometric and (p, q)-trigonometric functions were introduced by Lindqvist and Takeuchi, respectively.
引用
收藏
页码：473 / 484
页数：12
相关论文
共 50 条
  • [1] Convexity properties of generalized trigonometric and hyperbolic functions
    Árpád Baricz
    Barkat Ali Bhayo
    Riku Klén
    [J]. Aequationes mathematicae, 2015, 89 : 473 - 484
  • [2] A SURVEY FOR GENERALIZED TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS
    Yin, Li
    Huang, Li-Guo
    Wang, Yong-Li
    Lin, Xiu-Li
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2019, 13 (03): : 833 - 854
  • [3] Parameter convexity and concavity of generalized trigonometric functions
    Karp, D. B.
    Prilepkina, E. G.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 421 (01) : 370 - 382
  • [4] Inequalities for the generalized trigonometric and hyperbolic functions
    Klen, Riku
    Vuorinen, Matti
    Zhang, Xiaohui
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (01) : 521 - 529
  • [5] Inequalities on generalized trigonometric and hyperbolic functions
    Yang, Chen-Yan
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 419 (02) : 775 - 782
  • [6] Inequalities for the generalized trigonometric and hyperbolic functions
    Ma, Xiaoyan
    Si, Xiangbin
    Zhong, Genhong
    He, Jianhui
    [J]. OPEN MATHEMATICS, 2020, 18 : 1580 - 1589
  • [7] A NOTE ON GENERALIZED TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS
    Song, Ying-Qing
    Chu, Yu-Ming
    Liu, Bao-Yu
    Wang, Miao-Kun
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2014, 8 (03): : 635 - 642
  • [8] INEQUALITIES INVOLVING GENERALIZED TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS
    Neuman, Edward
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2014, 8 (04): : 725 - 736
  • [9] Some inequalities for the generalized trigonometric and hyperbolic functions
    Sun, Bao-ju
    [J]. PROCEEDINGS OF THE 2016 INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND ELECTRONIC TECHNOLOGY, 2016, 48 : 251 - 254
  • [10] Properties of generalized trigonometric functions
    Edmunds, David E.
    Gurka, Petr
    Lang, Jan
    [J]. JOURNAL OF APPROXIMATION THEORY, 2012, 164 (01) : 47 - 56
12345