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 54 条
[1]  
Agarwal P., 2020, MATHEMATICS-BASEL, V8, P1
[2]   Monotonicity theorems and inequalities for the complete elliptic integrals\ [J].
Alzer, H ;
Qiu, SL .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 172 (02) :289-312
[3]  
ANDERSON G. D., 1997, Conformal Invariants, Inequalities, and Quasiconformal Maps
[4]   2D approximately reciprocal ρ-convex functions and associated integral inequalities [J].
Awan, Muhammad Uzair ;
Akhtar, Nousheen ;
Kashuri, Artion ;
Noor, Muhammad Aslam ;
Chu, Yu-Ming .
AIMS MATHEMATICS, 2020, 5 (05) :4662-4680
[5]   Some New Refinements of Hermite-Hadamard-Type Inequalities Involving ψk-Riemann-Liouville Fractional Integrals and Applications [J].
Awan, Muhammad Uzair ;
Talib, Sadia ;
Chu Yu-Ming ;
Noor, Muhammad Aslam ;
Noor, Khalida Inayat .
MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020
[6]   New Hermite-Hadamard type inequalities for n-polynomial harmonically convex functions [J].
Awan, Muhammad Uzair ;
Akhtar, Nousheen ;
Iftikhar, Sabah ;
Noor, Muhammad Aslam ;
Chu, Yu-Ming .
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2020, 2020 (01)
[7]   A variant of Jensen-type inequality and related results for harmonic convex functions [J].
Baloch, Imran Abbas ;
Mughal, Aqeel Ahmad ;
Chu, Yu-Ming ;
Ul Haq, Absar ;
De La Sen, Manuel .
AIMS MATHEMATICS, 2020, 5 (06) :6404-6418
[8]   Petrovic-Type Inequalities for Harmonic h-convex Functions [J].
Baloch, Imran Abbas ;
Chu, Yu-Ming .
JOURNAL OF FUNCTION SPACES, 2020, 2020
[9]  
Berndt BC., 1989, Ramanujan's Notebooks
[10]   Bounds for the Remainder in Simpson's Inequality vian-Polynomial Convex Functions of Higher Order Using Katugampola Fractional Integrals [J].
Chu, Yu-Ming ;
Awan, Muhammad Uzair ;
Javad, Muhammad Zakria ;
Khan, Awais Gul .
JOURNAL OF MATHEMATICS, 2020, 2020
123456