Properties of generalized $ (p, q) $-elliptic integrals and generalized $ (p, q) $-Hersch-Pfluger distortion function

Chuan-Yu Cai; Qiu-Ying Zhang; Ti-Ren Huang; Chuan-Yu Cai; Qiu-Ying Zhang; Ti-Ren Huang

doi:10.3934/math.20231597

AIMS Mathematics

2023, Volume 8, Issue 12: 31198-31216. doi: 10.3934/math.20231597

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Research article Special Issues

Properties of generalized $ (p, q) $-elliptic integrals and generalized $ (p, q) $-Hersch-Pfluger distortion function

1.
Zhejiang Technical Institute of Economics, Hangzhou, 310018, China
2.
The Open University of Jinhua, Jinhua, 321000, China
3.
Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

Received: 23 July 2023 Revised: 27 October 2023 Accepted: 14 November 2023 Published: 23 November 2023
MSC : 33C05, 33E05

In this paper, we focus on investigating various properties of generalized $ (p, q) $-elliptic integrals and the generalized $ (p, q) $-Hersch-Pfluger distortion function. We establish the complete monotonicity, logarithmic, geometric concavity, and convexity of certain functions involving these generalized integrals and arcsine functions. Additionally, we derive several precise inequalities for the generalized $ (p, q) $-Hersch-Pfluger distortion function, which enhance and extend previous results.
- generalized $ (p, q) $-elliptic integrals,
- generalized $ (p, q) $-Hersch-Pfluger distortion function,
- convexity,
- concavity,
- monotonicity,
- logarithmic
Citation: Chuan-Yu Cai, Qiu-Ying Zhang, Ti-Ren Huang. Properties of generalized $ (p, q) $-elliptic integrals and generalized $ (p, q) $-Hersch-Pfluger distortion function[J]. AIMS Mathematics, 2023, 8(12): 31198-31216. doi: 10.3934/math.20231597

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Abstract

In this paper, we focus on investigating various properties of generalized $ (p, q) $-elliptic integrals and the generalized $ (p, q) $-Hersch-Pfluger distortion function. We establish the complete monotonicity, logarithmic, geometric concavity, and convexity of certain functions involving these generalized integrals and arcsine functions. Additionally, we derive several precise inequalities for the generalized $ (p, q) $-Hersch-Pfluger distortion function, which enhance and extend previous results.

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