Monotonicity, convexity and inequalities related to complete (p, q, r)-elliptic integrals and generalized trigonometric functions

被引：5
|
作者：
Yin, Li [1 ]
Lin, Xiu-Li [2 ]
Qi, Feng [3 ,4 ]
机构：
[1] Binzhou Univ, Coll Sci, Binzhou 256603, Shandong, Peoples R China
[2] Qufu Normal Univ, Coll Math Sci, Qufu 273165, Shandong, Peoples R China
[3] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China
[4] Tianjin Polytech Univ, Sch Math Sci, Tianjin 300387, Peoples R China
来源：
PUBLICATIONES MATHEMATICAE DEBRECEN | 2020年 / 97卷 / 1-2期
基金：
中国国家自然科学基金;
关键词：
monotonicity; logarithmic convexity; geometric convexity; complete monotonicity; logarithmic mean inequality; identric mean inequality; Turan-type inequality; complete; (p; q; r)-elliptic integral; generalized trigonometric function; COMPLETE ELLIPTIC INTEGRALS; TURAN TYPE INEQUALITIES; PROPERTY;
D O I：
10.5486/PMD.2020.8793
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper, making use of the monotonicity theorem for the ratio of two power series, the Cebysev integral inequality for monotonic functions and the Hermite-Hadamard integral inequality for convex functions, the authors establish monotonicity, logarithmic and geometric convexity and concavity, logarithmic and identric mean inequalities, the Turan-type inequalities, and complete monotonicity of several functions involving complete (p, q, r)-elliptic integrals and generalized arcsine and arctangent functions.
引用
收藏
页码：181 / 199
页数：19
相关论文
共 50 条
  • [21] Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function
    Zhen-Hang Yang
    Jing-Feng Tian
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113 : 3603 - 3617
  • [22] INEQUALITIES AND COMPLETE MONOTONICITY FOR THE GAMMA AND RELATED FUNCTIONS
    Chen, Chao-Ping
    Choi, Junesang
    COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2019, 34 (04): : 1261 - 1278
  • [23] Turan type inequalities for generalized complete elliptic integrals
    Baricz, Arpad
    MATHEMATISCHE ZEITSCHRIFT, 2007, 256 (04) : 895 - 911
  • [24] ON GENERALIZED COMPLETE ELLIPTIC INTEGRALS AND MODULAR FUNCTIONS
    Bhayo, B. A.
    Vuorinen, M.
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2012, 55 : 591 - 611
  • [25] Monotonicity properties and bounds for the complete p-elliptic integrals
    Ti-Ren Huang
    Shen-Yang Tan
    Xiao-Yan Ma
    Yu-Ming Chu
    Journal of Inequalities and Applications, 2018
  • [26] Monotonicity properties and bounds for the complete p-elliptic integrals
    Huang, Ti-Ren
    Tan, Shen-Yang
    Ma, Xiao-Yan
    Chu, Yu-Ming
    JOURNAL OF INEQUALITIES AND APPLICATIONS, 2018,
  • [27] Monotonicity properties and bounds for the complete p-elliptic integrals
    Huang, Xi-Fan
    Wang, Miao-Kun
    Shao, Hao
    Zhao, Yi-Fan
    Chu, Yu-Ming
    AIMS MATHEMATICS, 2020, 5 (06): : 7071 - 7086
  • [28] Monotonicity and inequalities related to complete elliptic integrals of the second kind (vol 5, pg 2732, 2020)
    Wang, Fei
    Guo, Bai-Ni
    Qi, Feng
    AIMS MATHEMATICS, 2020, 5 (06): : 5683 - 5684
  • [29] Functional Inequalities for Generalized Complete Elliptic Integrals with Two Parameters
    Dou, Xiangkai
    Yin, Li
    Lin, Xiu-Li
    JOURNAL OF FUNCTION SPACES, 2019, 2019
  • [30] Turán type inequalities for generalized complete elliptic integrals
    Árpád Baricz
    Mathematische Zeitschrift, 2007, 256
12345