MDPI - Publisher of Open Access Journals

29 pages, 939 KiB

Open AccessArticle

Sharp Power Mean Bounds for Two Seiffert-like Means

by Zhenhang Yang and Jing Zhang

Axioms 2023, 12(10), 910; https://doi.org/10.3390/axioms12100910 - 25 Sep 2023

Cited by 1 | Viewed by 1241

The mean is a subject of extensive study among scholars, and the pursuit of optimal power mean bounds is a highly active field. This article begins with a concise overview of recent advancements in this area, focusing specifically on Seiffert-like means. We establish sharp power mean bounds for two Seiffert-like means, including the introduction and establishment of the best asymmetric mean bounds for symmetric means. Additionally, we explore the practical applications of these findings by extending several intriguing chains of inequalities that involve more than ten means. This comprehensive analysis provides a deeper understanding of the relationships and properties of these means. Full article

(This article belongs to the Special Issue Mathematical Analysis in Application to Solving Mathematical and Technical Problems)

► Show Figures

Figure 1

16 pages, 294 KiB

Open AccessArticle

New Masjed Jamei–Type Inequalities for Inverse Trigonometric and Inverse Hyperbolic Functions

by Ling Zhu

Mathematics 2022, 10(16), 2972; https://doi.org/10.3390/math10162972 - 17 Aug 2022

Cited by 5 | Viewed by 1656

Abstract

In this paper, we establish two new inequalities of the Masjed Jamei type for inverse trigonometric and inverse hyperbolic functions and apply them to obtain some refinement and extension of Mitrinović–Adamović and Lazarević inequalities. The inequalities obtained in this paper go beyond the conclusions and conjectures in the previous literature. Finally, we apply the main results of this paper to the field of mean value inequality and obtain two new inequalities on Seiffert-like means and classical means. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

12 pages, 281 KiB

Open AccessArticle

Several Double Inequalities for Integer Powers of the Sinc and Sinhc Functions with Applications to the Neuman–Sándor Mean and the First Seiffert Mean

by Wen-Hui Li, Qi-Xia Shen and Bai-Ni Guo

Axioms 2022, 11(7), 304; https://doi.org/10.3390/axioms11070304 - 23 Jun 2022

Cited by 8 | Viewed by 3343

Abstract

In the paper, the authors establish a general inequality for the hyperbolic functions, extend the newly-established inequality to trigonometric functions, obtain some new inequalities involving the inverse sine and inverse hyperbolic sine functions, and apply these inequalities to the Neuman–Sándor mean and the [...] Read more.

(This article belongs to the Special Issue A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi)

14 pages, 267 KiB

Open AccessArticle

New Bounds for Arithmetic Mean by the Seiffert-like Means

by Ling Zhu

Mathematics 2022, 10(11), 1789; https://doi.org/10.3390/math10111789 - 24 May 2022

Cited by 1 | Viewed by 1662

Abstract

By using the power series of the functions

1 / {sin}^{n} t

and

(cos t) / ({sin}^{n} t)

(

n = 1, 2, 3, 4, 5

), and the estimation of the ratio of two adjacent Bernoulli [...] Read more.

By using the power series of the functions

1 / {sin}^{n} t

and

(cos t) / ({sin}^{n} t)

(

n = 1, 2, 3, 4, 5

), and the estimation of the ratio of two adjacent Bernoulli numbers, we obtained new bounds for arithmetic mean

A

by the weighted arithmetic means of

M_{tan}^{1 / 3} M_{sin}^{2 / 3}

and

\frac{1}{3} M_{tan} + \frac{2}{3} M_{sin},

M_{tanh}^{1 / 3} M_{sinh}^{2 / 3}

and

\frac{1}{3} M_{tanh} + \frac{2}{3} M_{sinh},

where

M_{tan} (x, y)

and

M_{sin} (x, y)

M_{tanh} (x, y)

and

M_{sinh} (x, y)

are the tangent mean, sine mean, hyperbolic tangent mean and hyperbolic sine mean, respectively. The upper and lower bounds obtained in this paper are compared in detail with the conclusions of the previous literature. Full article

(This article belongs to the Section E1: Mathematics and Computer Science)

Search Results (4)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (4)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI