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Axioms
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Current Research on Mathematical Inequalities
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Current Research on Mathematical Inequalities

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 35909
Please contact the Guest Editor or the Journal Editor ([email protected]) for any queries about the scope, discount, submission procedure and publication process.

Special Issue Editor

Dr. Christophe Chesneau

E-Mail Website
Guest Editor
Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, 14032 Caen, France
Interests: mathematical statistics; applied statistics; data analysis; probability; applied probability; analytic inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

There are many types of inequalities: Bernoulli's inequality, the Cauchy–Schwarz inequality, Hölder's inequality, the inequality of arithmetic and geometric means, the Minkowski inequality, etc. Mathematical inequalities have always played a major role in all branches of mathematics. They are often used to bind important but unmanageable mathematical terms of interest, with other mathematical terms being simple enough to draw some conclusions.

The aim of our Special Issue, titled "Current Research on Mathematical Inequalities", is to collect important research on all kinds of mathematical inequalities. Pure mathematical inequalities, applied mathematical inequalities, and/or solid conjectural inequalities are welcome. Only impeccably written and arranged papers of exceptional quality,  featuring novel research findings will be considered.

The research topics include, but are not limited to, the following: conjectural inequalities with numerical evidence, inequalities in analysis (sophisticated or not, with special functions or not, applied or not), inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in number theory, inequalities in optimization, inequalities in physics, inequalities in probability, and inequalities in statistics.

Dr. Christophe Chesneau
Guest Editor

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. Axioms 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

  • inequalities in theoretical mathematics
  • inequalities in applied mathematics
  • inequalities in physics
  • inequalities in probability and statistics
  • conjectural inequality with numerical evidence

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Related Special Issue

Published Papers (18 papers)

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Editorial

Jump to: Research

3 pages, 161 KiB  
Editorial
Introduction to the Special Issue in Axioms Titled Current Research on Mathematical Inequalities
by Christophe Chesneau
Axioms 2023, 12(2), 109; https://doi.org/10.3390/axioms12020109 - 19 Jan 2023
Viewed by 828
Abstract
The importance of inequalities in Mathematics is beautifully summarized in a citation attributed to Respected Professor Andrey Nikolaevich Kolmogorov: [...] Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)

Research

Jump to: Editorial

17 pages, 314 KiB  
Article
Some New Estimates for the Berezin Number of Hilbert Space Operators
by Najla Altwaijry, Kais Feki and Nicuşor Minculete
Axioms 2022, 11(12), 683; https://doi.org/10.3390/axioms11120683 - 29 Nov 2022
Cited by 4 | Viewed by 1427
Abstract
In this paper, we have developed new estimates of some estimates involving the Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space HΩ. The uniqueness or novelty of this article consists of new estimates [...] Read more.
In this paper, we have developed new estimates of some estimates involving the Berezin norm and Berezin number of bounded linear operators defined on a reproducing kernel Hilbert space HΩ. The uniqueness or novelty of this article consists of new estimates of Berezin numbers for different types of operators. These estimates improve the upper bounds of the Berezin numbers obtained by other similar papers. We give several upper bounds for berr(S*T), where T,S∈B(HΩ) and r≥1. We also present an estimation of ber2r∑i=1dTi where Ti∈B(HΩ), i=1,d¯ and r≥1. Some of the obtained inequalities represent improvements to earlier ones. In this work, the ideas and methodologies presented may serve as a starting point for future investigation in this field. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
20 pages, 351 KiB  
Article
Operator Jensen’s Inequality for Operator Superquadratic Functions
by Mohammad W. Alomari, Christophe Chesneau and Ahmad Al-Khasawneh
Axioms 2022, 11(11), 617; https://doi.org/10.3390/axioms11110617 - 6 Nov 2022
Cited by 2 | Viewed by 1410
Abstract
In this work, an operator superquadratic function (in the operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. A general Bohr’s inequality for [...] Read more.
In this work, an operator superquadratic function (in the operator sense) for positive Hilbert space operators is defined. Several examples with some important properties together with some observations which are related to the operator convexity are pointed out. A general Bohr’s inequality for positive operators is thus deduced. A Jensen-type inequality is proved. Equivalent statements of a non-commutative version of Jensen’s inequality for operator superquadratic function are also established. Finally, several trace inequalities for superquadratic functions (in the ordinary sense) are provided as well. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
12 pages, 307 KiB  
Article
On Symmetrized Stochastic Harmonically Convexity and Hermite–Hadamard Type Inequalities
by Muhammad Amer Latif
Axioms 2022, 11(10), 570; https://doi.org/10.3390/axioms11100570 - 20 Oct 2022
Cited by 3 | Viewed by 1525
Abstract
Throughout this study, the concept of symmetrized harmonically convex stochastic processes will be discussed in further detail. Some certain characterizations for symmetrized harmonically convex stochastic processes are discussed that use Hermite–Hadamard-type inequalities. A Hyers–Ulam-type stability result for harmonically convex stochastic processes is given [...] Read more.
Throughout this study, the concept of symmetrized harmonically convex stochastic processes will be discussed in further detail. Some certain characterizations for symmetrized harmonically convex stochastic processes are discussed that use Hermite–Hadamard-type inequalities. A Hyers–Ulam-type stability result for harmonically convex stochastic processes is given as well. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
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15 pages, 291 KiB  
Article
Weighted Integral Inequalities for Harmonic Convex Functions in Connection with Fejér’s Result
by Muhammad Amer Latif
Axioms 2022, 11(10), 564; https://doi.org/10.3390/axioms11100564 - 18 Oct 2022
Cited by 5 | Viewed by 1303
Abstract
In this study, on the subject of harmonic convex functions, we introduce some new functionals linked with weighted integral inequalities for harmonic convex functions. In addition, certain new inequalities of the Fejér type are discovered. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
11 pages, 773 KiB  
Article
Univariate and Multivariate Ostrowski-Type Inequalities Using Atangana–Baleanu Caputo Fractional Derivative
by Henok Desalegn Desta, Deepak B. Pachpatte, Jebessa B. Mijena and Tadesse Abdi
Axioms 2022, 11(9), 482; https://doi.org/10.3390/axioms11090482 - 19 Sep 2022
Cited by 4 | Viewed by 1511
Abstract
In this paper, we obtain some univariate and multivariate Ostrowski-type inequalities using the Atangana–Baleanu fractional derivative in the sense of Liouville–Caputo (ABC). The results obtained for both left and right ABC fractional derivatives can be applied to study further fractional inequalities and estimate [...] Read more.
In this paper, we obtain some univariate and multivariate Ostrowski-type inequalities using the Atangana–Baleanu fractional derivative in the sense of Liouville–Caputo (ABC). The results obtained for both left and right ABC fractional derivatives can be applied to study further fractional inequalities and estimate various non-local function problems since the operator consists of a non-singular kernel. The obtained results are more generalized in nature. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
16 pages, 356 KiB  
Article
Interval Fejér-Type Inequalities for Left and Right-λ-Preinvex Functions in Interval-Valued Settings
by Tareq Saeed, Muhammad Bilal Khan, Savin Treanțǎ, Hamed H. Alsulami and Mohammed Sh. Alhodaly
Axioms 2022, 11(8), 368; https://doi.org/10.3390/axioms11080368 - 27 Jul 2022
Cited by 18 | Viewed by 1536
Abstract
For left and right λ-preinvex interval-valued functions (left and right λ-preinvex IVFs) in interval-valued Riemann operator settings, we create Hermite–Hadamard (H-H) type inequalities in the current study. Additionally, we create Hermite–Hadamard–Fejér (H-H-Fejér)-type inequalities [...] Read more.
For left and right λ-preinvex interval-valued functions (left and right λ-preinvex IVFs) in interval-valued Riemann operator settings, we create Hermite–Hadamard (H-H) type inequalities in the current study. Additionally, we create Hermite–Hadamard–Fejér (H-H-Fejér)-type inequalities for preinvex functions of the left and right interval-valued type under some mild conditions. Moreover, some exceptional new and classical cases are also obtained. Some useful examples are also presented to prove the validity of the results. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
16 pages, 334 KiB  
Article
New Diamond-α Steffensen-Type Inequalities for Convex Functions over General Time Scale Measure Spaces
by Ksenija Smoljak Kalamir
Axioms 2022, 11(7), 323; https://doi.org/10.3390/axioms11070323 - 1 Jul 2022
Cited by 6 | Viewed by 1438
Abstract
In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-finite measures in time scale calculus. Moreover, as a special case, we [...] Read more.
In this paper, we extend some Steffensen-type inequalities to time scales by using the diamond-α-dynamic integral. Further, we prove some new Steffensen-type inequalities for convex functions utilizing positive σ-finite measures in time scale calculus. Moreover, as a special case, we obtain these inequalities for the delta and the nabla integral. By using the relation between calculus on time scales T and differential calculus on R, we obtain already-known Steffensen-type inequalities. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
16 pages, 293 KiB  
Article
Some Generalized Euclidean Operator Radius Inequalities
by Mohammad W. Alomari, Khalid Shebrawi and Christophe Chesneau
Axioms 2022, 11(6), 285; https://doi.org/10.3390/axioms11060285 - 13 Jun 2022
Cited by 9 | Viewed by 1895
Abstract
In this work, some generalized Euclidean operator radius inequalities are established. Refinements of some well-known results are provided. Among others, some bounds in terms of the Cartesian decomposition of a given Hilbert space operator are proven. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
13 pages, 319 KiB  
Article
Bounds for Quotients of Inverse Trigonometric and Inverse Hyperbolic Functions
by Sumedh B. Thool, Yogesh J. Bagul, Ramkrishna M. Dhaigude and Christophe Chesneau
Axioms 2022, 11(6), 262; https://doi.org/10.3390/axioms11060262 - 30 May 2022
Cited by 2 | Viewed by 1729
Abstract
We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin−1xsinh−1x and tanh−1xtan−1x. The main results provide polynomial bounds using even [...] Read more.
We establish new simple bounds for the quotients of inverse trigonometric and inverse hyperbolic functions such as sin−1xsinh−1x and tanh−1xtan−1x. The main results provide polynomial bounds using even quadratic functions and exponential bounds under the form eax2. Graph validation is also performed. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
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17 pages, 321 KiB  
Article
Some Generalizations of the Jensen-Type Inequalities with Applications
by Mirna Rodić
Axioms 2022, 11(5), 227; https://doi.org/10.3390/axioms11050227 - 13 May 2022
Cited by 5 | Viewed by 2142
Abstract
Motivated by some results about reverses of the Jensen inequality for positive measure, in this paper we give generalizations of those results for real Stieltjes measure dλ which is not necessarily positive using several Green functions. Utilizing these results we define some [...] Read more.
Motivated by some results about reverses of the Jensen inequality for positive measure, in this paper we give generalizations of those results for real Stieltjes measure dλ which is not necessarily positive using several Green functions. Utilizing these results we define some new mean value theorems of Lagrange and Cauchy types, and derive some new Cauchy-type means. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
8 pages, 280 KiB  
Article
Coefficient Estimates and Fekete–Szegö Functional Inequalities for a Certain Subclass of Analytic and Bi-Univalent Functions
by Mohamed Illafe, Ala Amourah and Maisarah Haji Mohd
Axioms 2022, 11(4), 147; https://doi.org/10.3390/axioms11040147 - 24 Mar 2022
Cited by 18 | Viewed by 2469
Abstract
The present paper introduces a new class of bi-univalent functions defined on a symmetric domain using Gegenbauer polynomials. For functions in this class, we have derived the estimates of the Taylor–Maclaurin coefficients, a2 and a3, and the Fekete-Szegö functional. Several [...] Read more.
The present paper introduces a new class of bi-univalent functions defined on a symmetric domain using Gegenbauer polynomials. For functions in this class, we have derived the estimates of the Taylor–Maclaurin coefficients, a2 and a3, and the Fekete-Szegö functional. Several new results follow upon specializing the parameters involved in our main results. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
9 pages, 251 KiB  
Article
On Some New Ostrowski–Mercer-Type Inequalities for Differentiable Functions
by Ifra Bashir Sial, Nichaphat Patanarapeelert, Muhammad Aamir Ali, Hüseyin Budak and Thanin Sitthiwirattham
Axioms 2022, 11(3), 132; https://doi.org/10.3390/axioms11030132 - 14 Mar 2022
Cited by 10 | Viewed by 2251
Abstract
In this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski–Mercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of [...] Read more.
In this paper, we establish a new integral identity involving differentiable functions, and then we use the newly established identity to prove some Ostrowski–Mercer-type inequalities for differentiable convex functions. It is also demonstrated that the newly established inequalities are generalizations of some of the Ostrowski inequalities established inside the literature. There are also some applications to the special means of real numbers given. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
17 pages, 651 KiB  
Article
K-Nearest Neighbor Estimation of Functional Nonparametric Regression Model under NA Samples
by Xueping Hu, Jingya Wang, Liuliu Wang and Keming Yu
Axioms 2022, 11(3), 102; https://doi.org/10.3390/axioms11030102 - 25 Feb 2022
Cited by 7 | Viewed by 3570
Abstract
Functional data, which provides information about curves, surfaces or anything else varying over a continuum, has become a commonly encountered type of data. The k-nearest neighbor (kNN) method, as a nonparametric method, has become one of the most popular supervised machine learning algorithms [...] Read more.
Functional data, which provides information about curves, surfaces or anything else varying over a continuum, has become a commonly encountered type of data. The k-nearest neighbor (kNN) method, as a nonparametric method, has become one of the most popular supervised machine learning algorithms used to solve both classification and regression problems. This paper is devoted to the k-nearest neighbor (kNN) estimators of the nonparametric functional regression model when the observed variables take values from negatively associated (NA) sequences. The consistent and complete convergence rate for the proposed kNN estimator is first provided. Then, numerical assessments, including simulation study and real data analysis, are conducted to evaluate the performance of the proposed method and compare it with the standard nonparametric kernel approach. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
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8 pages, 255 KiB  
Article
Pólya–Szegö Integral Inequalities Using the Caputo–Fabrizio Approach
by Asha B. Nale, Vaijanath L. Chinchane, Satish K. Panchal and Christophe Chesneau
Axioms 2022, 11(2), 79; https://doi.org/10.3390/axioms11020079 - 17 Feb 2022
Cited by 2 | Viewed by 1733
Abstract
In this article, we establish some of the Pólya–Szegö and Minkowsky-type fractional integral inequalities by considering the Caputo–Fabrizio fractional integral. Moreover, we give some special cases of Pólya–Szegö inequalities. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
9 pages, 378 KiB  
Article
Perturbation of One-Dimensional Time-Independent Schrödinger Equation with a Near-Hyperbolic Potential
by Byungbae Kim and Soon-Mo Jung
Axioms 2022, 11(2), 63; https://doi.org/10.3390/axioms11020063 - 2 Feb 2022
Cited by 2 | Viewed by 2088
Abstract
The authors have recently investigated a type of Hyers–Ulam stability of one-dimensional time-independent Schrödinger equation with a symmetric parabolic potential wall. In this paper, we investigate a type of Hyers–Ulam stability of the Schrödinger equation with a near-hyperbolic potential. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
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18 pages, 305 KiB  
Article
Post-Quantum Midpoint-Type Inequalities Associated with Twice-Differentiable Functions
by Thanin Sitthiwirattham, Ghulam Murtaza, Muhammad Aamir Ali, Chanon Promsakon, Ifra Bashir Sial and Praveen Agarwal
Axioms 2022, 11(2), 46; https://doi.org/10.3390/axioms11020046 - 23 Jan 2022
Cited by 6 | Viewed by 2346
Abstract
In this study, first we establish a p,q-integral identity involving the second p,q-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-p,q-differentiable convex functions. It is also shown [...] Read more.
In this study, first we establish a p,q-integral identity involving the second p,q-derivative, and then, we use this result to prove some new midpoint-type inequalities for twice-p,q-differentiable convex functions. It is also shown that the newly established results are the refinements of the comparable results in the literature. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
8 pages, 256 KiB  
Article
A Note on Hermite–Hadamard–Fejer Type Inequalities for Functions Whose n-th Derivatives Are m-Convex or (α,m)-Convex Functions
by Sanja Kovač
Axioms 2022, 11(1), 16; https://doi.org/10.3390/axioms11010016 - 31 Dec 2021
Cited by 1 | Viewed by 1440
Abstract
In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensions and generalizations of the existing ones. [...] Read more.
In this paper, we develop some Hermite–Hadamard–Fejér type inequalities for n-times differentiable functions whose absolute values of n-th derivatives are (α,m)-convex function. The results obtained in this paper are extensions and generalizations of the existing ones. As a special case, the generalization of the remainder term of the midpoint and trapezoidal quadrature formulas are obtained. Full article
(This article belongs to the Special Issue Current Research on Mathematical Inequalities)
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