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Symmetry
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Symmetry in the Mathematical Inequalities
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Symmetry in the Mathematical Inequalities

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (1 April 2022) | Viewed by 25436

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Dr. Nicusor Minculete

E-Mail Website
Guest Editor
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
Interests: inequalities; generalized entropies; Euclidean geometry; operator theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Shigeru Furuichi

E-Mail Website
Guest Editor
Department of Information Science, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo 156-8550, Japan
Interests: generalized entropies; inequalities; matrix analysis; operator theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The theory of inequalities represents a long-standing topic in many mathematical areas and remains an attractive research domain with many applications. This Special Issue brings together original research papers in all areas of mathematics that are concerned with inequalities or their role. The research results presented in this Special Issue are related to the improvement of classical inequalities and highlight their applications, promoting an exchange of ideas between mathematicians from many parts of the world dedicated to the theory of inequalities.

For example, the study of convex functions has occupied a central role in the theory of inequalities because such functions develop a series of inequalities. In number theory, a number of inequalities characterize arithmetic functions. Other important types of inequalities are those related to invertible positive operators that have applications in operator equations, network theory and quantum information theory (inequalities for generalized entropies).

Please note that all submitted papers should be within the scope of the journal.

Due to the great success of our Special Issue "Symmetry in the Mathematical Inequalities", we decided to set up a second volume. We invite you to contribute to the Special Issue "Inequality and Symmetry in Mathematical Analysis" by https://www.mdpi.com/journal/symmetry/special_issues/symmetry_mathematical_inequalities2.

Dr. Nicusor Minculete
Prof. Dr. Shigeru Furuichi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • analytical inequalities
  • functional inequalities
  • convexity
  • differential and difference inequalities
  • means
  • operator theory
  • approximation theory
  • number theory
  • generalized entropies

Published Papers (16 papers)

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Editorial

Jump to: Research

5 pages, 189 KiB  
Editorial
Special Issue Editorial “Symmetry in the Mathematical Inequalities”
by Nicuşor Minculete
Symmetry 2022, 14(4), 774; https://doi.org/10.3390/sym14040774 - 8 Apr 2022
Viewed by 1338
Abstract
The theory of inequalities represents a long-standing topic in many mathematical areas and remains an attractive research domain with many applications [...] Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)

Research

Jump to: Editorial

23 pages, 858 KiB  
Article
New Generalized Class of Convex Functions and Some Related Integral Inequalities
by Artion Kashuri, Ravi P. Agarwal, Pshtiwan Othman Mohammed, Kamsing Nonlaopon, Khadijah M. Abualnaja and Yasser S. Hamed
Symmetry 2022, 14(4), 722; https://doi.org/10.3390/sym14040722 - 2 Apr 2022
Cited by 6 | Viewed by 1579
Abstract
There is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the (n,m)–generalized convex and studied its basic algebraic properties. The Hermite–Hadamard inequality for the [...] Read more.
There is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the (n,m)–generalized convex and studied its basic algebraic properties. The Hermite–Hadamard inequality for the (n,m)–generalized convex function, for the products of two functions and of this type, were proven. Moreover, this class of functions was applied to several known identities; midpoint-type inequalities of Ostrowski and Simpson were derived. Our results are extensions of many previous contributions related to integral inequalities via different convexities. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
13 pages, 278 KiB  
Article
On Generalization of Different Integral Inequalities for Harmonically Convex Functions
by Jiraporn Reunsumrit, Miguel J. Vivas-Cortez, Muhammad Aamir Ali and Thanin Sitthiwirattham
Symmetry 2022, 14(2), 302; https://doi.org/10.3390/sym14020302 - 2 Feb 2022
Cited by 2 | Viewed by 1411
Abstract
In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as [...] Read more.
In this study, we first prove a parameterized integral identity involving differentiable functions. Then, for differentiable harmonically convex functions, we use this result to establish some new inequalities of a midpoint type, trapezoidal type, and Simpson type. Analytic inequalities of this type, as well as the approaches for solving them, have applications in a variety of domains where symmetry is important. Finally, several particular cases of recently discovered results are discussed, as well as applications to the special means of real numbers. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
22 pages, 365 KiB  
Article
Spatial Decay Bounds for the Brinkman Fluid Equations in Double-Diffusive Convection
by Xuejiao Chen, Yuanfei Li and Dandan Li
Symmetry 2022, 14(1), 98; https://doi.org/10.3390/sym14010098 - 7 Jan 2022
Cited by 2 | Viewed by 1040
Abstract
In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, [...] Read more.
In this paper, we consider the Brinkman equations pipe flow, which includes the salinity and the temperature. Assuming that the fluid satisfies nonlinear boundary conditions at the finite end of the cylinder, using the symmetry of differential inequalities and the energy analysis methods, we establish the exponential decay estimates for homogeneous Brinkman equations. That is to prove that the solutions of the equation decay exponentially with the distance from the finite end of the cylinder. To make the estimate of decay explicit, the bound for the total energy is also derived. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
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17 pages, 312 KiB  
Article
On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus
by Miguel J. Vivas-Cortez, Muhammad Aamir Ali, Shahid Qaisar, Ifra Bashir Sial, Sinchai Jansem and Abdul Mateen
Symmetry 2021, 13(12), 2419; https://doi.org/10.3390/sym13122419 - 14 Dec 2021
Cited by 4 | Viewed by 1975
Abstract
In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type [...] Read more.
In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p,q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
19 pages, 326 KiB  
Article
Bounds for the Differences between Arithmetic and Geometric Means and Their Applications to Inequalities
by Shigeru Furuichi and Nicuşor Minculete
Symmetry 2021, 13(12), 2398; https://doi.org/10.3390/sym13122398 - 12 Dec 2021
Cited by 5 | Viewed by 1739
Abstract
Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means, using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We [...] Read more.
Refining and reversing weighted arithmetic-geometric mean inequalities have been studied in many papers. In this paper, we provide some bounds for the differences between the weighted arithmetic and geometric means, using known inequalities. We improve the results given by Furuichi-Ghaemi-Gharakhanlu and Sababheh-Choi. We also give some bounds on entropies, applying the results in a different approach. We explore certain convex or concave functions, which are symmetric functions on the axis t=1/2. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
13 pages, 303 KiB  
Article
Schur-Convexity for Elementary Symmetric Composite Functions and Their Inverse Problems and Applications
by Tao Zhang, Alatancang Chen, Huannan Shi, B. Saheya and Boyan Xi
Symmetry 2021, 13(12), 2351; https://doi.org/10.3390/sym13122351 - 7 Dec 2021
Cited by 1 | Viewed by 1902
Abstract
This paper investigates the Schur-convexity, Schur-geometric convexity, and Schur-harmonic convexity for the elementary symmetric composite function and its dual form. The inverse problems are also considered. New inequalities on special means are established by using the theory of majorization. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
22 pages, 311 KiB  
Article
Phragmén-Lindelöf Alternative Results for a Class of Thermoelastic Plate
by Shiguang Luo, Jincheng Shi and Baiping Ouyang
Symmetry 2021, 13(12), 2256; https://doi.org/10.3390/sym13122256 - 26 Nov 2021
Cited by 1 | Viewed by 1092
Abstract
The spatial properties of solutions for a class of thermoelastic plate with biharmonic operator were studied. The energy method was used. We constructed an energy expression. A differential inequality which the energy expression was controlled by a second-order differential inequality is deduced. The [...] Read more.
The spatial properties of solutions for a class of thermoelastic plate with biharmonic operator were studied. The energy method was used. We constructed an energy expression. A differential inequality which the energy expression was controlled by a second-order differential inequality is deduced. The Phragme´n-Lindelo¨f alternative results of the solutions were obtained by solving the inequality. These results show that the Saint-Venant principle is also valid for the hyperbolic–hyperbolic coupling equations. Our results can been seen as a version of symmetry in inequality for studying the Phragme´n-Lindelo¨f alternative results. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
13 pages, 291 KiB  
Article
Some New Simpson’s-Formula-Type Inequalities for Twice-Differentiable Convex Functions via Generalized Fractional Operators
by Muhammad Aamir Ali, Hasan Kara, Jessada Tariboon, Suphawat Asawasamrit, Hüseyin Budak and Fatih Hezenci
Symmetry 2021, 13(12), 2249; https://doi.org/10.3390/sym13122249 - 25 Nov 2021
Cited by 20 | Viewed by 1499
Abstract
From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable [...] Read more.
From the past to the present, various works have been dedicated to Simpson’s inequality for differentiable convex functions. Simpson-type inequalities for twice-differentiable functions have been the subject of some research. In this paper, we establish a new generalized fractional integral identity involving twice-differentiable functions, then we use this result to prove some new Simpson’s-formula-type inequalities for twice-differentiable convex functions. Furthermore, we examine a few special cases of newly established inequalities and obtain several new and old Simpson’s-formula-type inequalities. These types of analytic inequalities, as well as the methodologies for solving them, have applications in a wide range of fields where symmetry is crucial. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
9 pages, 240 KiB  
Article
Global Bounds for the Generalized Jensen Functional with Applications
by Slavko Simić and Bandar Bin-Mohsin
Symmetry 2021, 13(11), 2105; https://doi.org/10.3390/sym13112105 - 6 Nov 2021
Cited by 1 | Viewed by 1013
Abstract
In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky [...] Read more.
In this article we give sharp global bounds for the generalized Jensen functional Jn(g,h;p,x). In particular, exact bounds are determined for the generalized power mean in terms from the class of Stolarsky means. As a consequence, we obtain the best possible global converses of quotients and differences of the generalized arithmetic, geometric and harmonic means. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
16 pages, 300 KiB  
Article
Continuous Dependence on the Heat Source of 2D Large-Scale Primitive Equations in Oceanic Dynamics
by Yuanfei Li and Peng Zeng
Symmetry 2021, 13(10), 1961; https://doi.org/10.3390/sym13101961 - 18 Oct 2021
Cited by 6 | Viewed by 1050
Abstract
In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the [...] Read more.
In this paper, we consider the initial-boundary value problem for the two-dimensional primitive equations of the large-scale oceanic dynamics. These models are often used to predict weather and climate change. Using the differential inequality technique, rigorous a priori bounds of solutions and the continuous dependence on the heat source are established. We show the application of symmetry in mathematical inequalities in practice. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
18 pages, 355 KiB  
Article
On Some New Inequalities of Hermite–Hadamard Midpoint and Trapezoid Type for Preinvex Functions in p,q-Calculus
by Ifra Bashir Sial, Muhammad Aamir Ali, Ghulam Murtaza, Sotiris K. Ntouyas, Jarunee Soontharanon and Thanin Sitthiwirattham
Symmetry 2021, 13(10), 1864; https://doi.org/10.3390/sym13101864 - 3 Oct 2021
Cited by 6 | Viewed by 1400
Abstract
In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in [...] Read more.
In this paper, we establish some new Hermite–Hadamard type inequalities for preinvex functions and left-right estimates of newly established inequalities for p,q-differentiable preinvex functions in the context of p,q-calculus. We also show that the results established in this paper are generalizations of comparable results in the literature of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
22 pages, 313 KiB  
Article
On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables
by Thanin Sitthiwirattham, Hüseyin Budak, Hasan Kara, Muhammad Aamir Ali and Jiraporn Reunsumrit
Symmetry 2021, 13(9), 1724; https://doi.org/10.3390/sym13091724 - 17 Sep 2021
Cited by 4 | Viewed by 1266
Abstract
In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for [...] Read more.
In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann–Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
12 pages, 301 KiB  
Article
On Some New Trapezoidal Type Inequalities for Twice (p, q) Differentiable Convex Functions in Post-Quantum Calculus
by Thanin Sitthiwirattham, Ghulam Murtaza, Muhammad Aamir Ali, Sotiris K. Ntouyas, Muhammad Adeel and Jarunee Soontharanon
Symmetry 2021, 13(9), 1605; https://doi.org/10.3390/sym13091605 - 1 Sep 2021
Cited by 3 | Viewed by 1457
Abstract
Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a p,q [...] Read more.
Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a p,q-integral identity involving the second p,q-derivative and then we used this result to prove some new trapezoidal type inequalities for twice p,q-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
13 pages, 271 KiB  
Article
A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum
by Xianyong Huang, Shanhe Wu and Bicheng Yang
Symmetry 2021, 13(8), 1548; https://doi.org/10.3390/sym13081548 - 23 Aug 2021
Cited by 2 | Viewed by 1535
Abstract
In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help [...] Read more.
In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler–Maclaurin summation formula and Abel’s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
18 pages, 350 KiB  
Article
New Ostrowski-Type Fractional Integral Inequalities via Generalized Exponential-Type Convex Functions and Applications
by Soubhagya Kumar Sahoo, Muhammad Tariq, Hijaz Ahmad, Jamshed Nasir, Hassen Aydi and Aiman Mukheimer
Symmetry 2021, 13(8), 1429; https://doi.org/10.3390/sym13081429 - 4 Aug 2021
Cited by 26 | Viewed by 2025
Abstract
Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for [...] Read more.
Recently, fractional calculus has been the center of attraction for researchers in mathematical sciences because of its basic definitions, properties and applications in tackling real-life problems. The main purpose of this article is to present some fractional integral inequalities of Ostrowski type for a new class of convex mapping. Specifically, n–polynomial exponentially s–convex via fractional operator are established. Additionally, we present a new Hermite–Hadamard fractional integral inequality. Some special cases of the results are discussed as well. Due to the nature of convexity theory, there exists a strong relationship between convexity and symmetry. When working on either of the concepts, it can be applied to the other one as well. Integral inequalities concerned with convexity have a lot of applications in various fields of mathematics in which symmetry has a great part to play. Finally, in applications, some new limits for special means of positive real numbers and midpoint formula are given. These new outcomes yield a few generalizations of the earlier outcomes already published in the literature. Full article
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
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