Monotonicity properties and bounds for the complete p-elliptic integrals

被引：15
|
作者：
Huang, Xi-Fan [1 ]
Wang, Miao-Kun [1 ]
Shao, Hao [1 ]
Zhao, Yi-Fan [1 ]
Chu, Yu-Ming [2 ,3 ]
机构：
[1] Huzhou Univ, Dept Math, Huzhou 313000, Peoples R China
[2] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China
[3] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China
来源：
AIMS MATHEMATICS | 2020年 / 5卷 / 06期
关键词：
complete elliptic integral; complete p-elliptic integral; generalized trigonometric function; monotonicity; bound; CONVEX-FUNCTIONS; INEQUALITIES; HADAMARD; REFINEMENTS;
D O I：
10.3934/math.2020453
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the article, we establish some monotonicity properties for certain functions involving the complete p-elliptic integrals of the first and second kinds, and find several sharp bounds for the p-elliptic integrals. Our results are the generalizations and improvements of some previously known results for the classical complete elliptic integrals.
引用
收藏
页码：7071 / 7086
页数：16
相关论文
共 50 条
  • [1] Monotonicity properties and bounds for the complete p-elliptic integrals
    Ti-Ren Huang
    Shen-Yang Tan
    Xiao-Yan Ma
    Yu-Ming Chu
    [J]. Journal of Inequalities and Applications, 2018
  • [2] Monotonicity properties and bounds for the complete p-elliptic integrals
    Huang, Ti-Ren
    Tan, Shen-Yang
    Ma, Xiao-Yan
    Chu, Yu-Ming
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
  • [3] Monotonicity and functional inequalities for the complete p-elliptic integrals
    Zhang, Xiaohui
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 453 (02) : 942 - 953
  • [4] Precise bounds for the weighted Holder mean of the complete p-elliptic integrals
    Wang, Miao-Kun
    Chu, Hong-Hu
    Chu, Yu-Ming
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 480 (02)
  • [5] Approximations related to the complete p-elliptic integrals
    Zhong, Genhong
    Ma, Xiaoyan
    Wang, Fei
    [J]. OPEN MATHEMATICS, 2022, 20 (01): : 1046 - 1056
  • [6] MONOTONICITY PROPERTIES AND BOUNDS INVOLVING THE COMPLETE ELLIPTIC INTEGRALS OF THE FIRST KIND
    Yang, Zhen-Hang
    Qian, Wei-Mao
    Chu, Yu-Ming
    [J]. MATHEMATICAL INEQUALITIES & APPLICATIONS, 2018, 21 (04): : 1185 - 1199
  • [7] Functional inequalities for the ratio of complete p-elliptic integrals
    Gu, Xiaoyan
    Zhang, Xiaohui
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 488 (01)
  • [8] Complete p-elliptic integrals and a computation formula πp of for p=4
    Takeuchi, Shingo
    [J]. RAMANUJAN JOURNAL, 2018, 46 (02): : 309 - 321
  • [9] Asymptotically sharp bounds for the complete p-elliptic integral of the first kind
    Huang, Ti-Ren
    Chen, Lu
    Chu, Yu -Ming
    [J]. HOKKAIDO MATHEMATICAL JOURNAL, 2022, 51 (02) : 189 - 210
  • [10] Monotonicity theorems and inequalities for the complete elliptic integrals\
    Alzer, H
    Qiu, SL
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 172 (02) : 289 - 312
12345