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Symmetry
Special Issues
Inequality and Symmetry in Mathematical Analysis
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Inequality and Symmetry in Mathematical Analysis

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

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 8479

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 Symmetry journal.

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

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Published Papers (5 papers)

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Research

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18 pages, 322 KiB  
Article
Novel Mean-Type Inequalities via Generalized Riemann-Type Fractional Integral for Composite Convex Functions: Some Special Examples
by Muzammil Mukhtar, Muhammad Yaqoob, Muhammad Samraiz, Iram Shabbir, Sina Etemad, Manuel De la Sen and Shahram Rezapour
Symmetry 2023, 15(2), 479; https://doi.org/10.3390/sym15020479 - 10 Feb 2023
Cited by 2 | Viewed by 1288
Abstract
This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. [...] Read more.
This study deals with a novel class of mean-type inequalities by employing fractional calculus and convexity theory. The high correlation between symmetry and convexity increases its significance. In this paper, we first establish an identity that is crucial in investigating fractional mean inequalities. Then, we establish the main results involving the error estimation of the Hermite–Hadamard inequality for composite convex functions via a generalized Riemann-type fractional integral. Such results are verified by choosing certain composite functions. These results give well-known examples in special cases. The main consequences can generalize many known inequalities that exist in other studies. Full article
(This article belongs to the Special Issue Inequality and Symmetry in Mathematical Analysis)
14 pages, 300 KiB  
Article
Ostrowski Type Inequalities via Some Exponentially s-Preinvex Functions on Time Scales with Applications
by Kin Keung Lai, Shashi Kant Mishra and Vandana Singh
Symmetry 2023, 15(2), 410; https://doi.org/10.3390/sym15020410 - 3 Feb 2023
Cited by 2 | Viewed by 1372
Abstract
Integral inequalities concerned with convexity have many applications in several fields of mathematics in which symmetry plays an important role. In the theory of convexity, there exist strong connections between convexity and symmetry. If we are working on one of the concepts, then [...] Read more.
Integral inequalities concerned with convexity have many applications in several fields of mathematics in which symmetry plays an important role. In the theory of convexity, there exist strong connections between convexity and symmetry. If we are working on one of the concepts, then it can be applied to the other of them. In this paper, we establish some novel generalizations of Ostrowski type inequalities for exponentially s-preinvex and s-preinvex functions on time scale by using Hölder inequality and Montgomery Identity. We also obtain applications to some special means. These results are motivated by the symmetric results obtained in the recent article by Abbasi and Anwar in 2022 on Ostrowski type inequalities for exponentially s-convex functions and s-convex functions on time scale. Moreover, we discuss several special cases of the results obtained in this paper. Full article
(This article belongs to the Special Issue Inequality and Symmetry in Mathematical Analysis)
9 pages, 237 KiB  
Article
Refined Hermite–Hadamard Inequalities and Some Norm Inequalities
by Kenjiro Yanagi
Symmetry 2022, 14(12), 2522; https://doi.org/10.3390/sym14122522 - 29 Nov 2022
Cited by 2 | Viewed by 1368
Abstract
It is well known that the Hermite–Hadamard inequality (called the HH inequality) refines the definition of convexity of function f(x) defined on [a,b] by using the integral of f(x) from a to b [...] Read more.
It is well known that the Hermite–Hadamard inequality (called the HH inequality) refines the definition of convexity of function f(x) defined on [a,b] by using the integral of f(x) from a to b. There are many generalizations or refinements of HH inequality. Furthermore HH inequality has many applications to several fields of mathematics, including numerical analysis, functional analysis, and operator inequality. Recently, we gave several types of refined HH inequalities and obtained inequalities which were satisfied by weighted logarithmic means. In this article, we give an N-variable Hermite–Hadamard inequality and apply to some norm inequalities under certain conditions. As applications, we obtain several inequalities which are satisfied by means defined by symmetry. Finally, we obtain detailed integral values. Full article
(This article belongs to the Special Issue Inequality and Symmetry in Mathematical Analysis)
18 pages, 320 KiB  
Article
On the Dragomir Extension of Furuta’s Inequality and Numerical Radius Inequalities
by Mohammad W. Alomari, Gabriel Bercu and Christophe Chesneau
Symmetry 2022, 14(7), 1432; https://doi.org/10.3390/sym14071432 - 12 Jul 2022
Cited by 3 | Viewed by 1491
Abstract
In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: wT≤12T+T*. It is [...] Read more.
In this work, some numerical radius inequalities based on the recent Dragomir extension of Furuta’s inequality are obtained. Some particular cases are also provided. Among others, the celebrated Kittaneh inequality reads: wT≤12T+T*. It is proved that wT≤12T+T*−12infx=1Tx,x12−T*x,x122, which improves on the Kittaneh inequality for symmetric and non-symmetric Hilbert space operators. Other related improvements to well-known inequalities in literature are also provided. Full article
(This article belongs to the Special Issue Inequality and Symmetry in Mathematical Analysis)

Review

Jump to: Research

24 pages, 908 KiB  
Review
A Review of Hermite–Hadamard Inequality for α-Type Real-Valued Convex Functions
by Ohud Almutairi and Adem Kılıçman
Symmetry 2022, 14(5), 840; https://doi.org/10.3390/sym14050840 - 19 Apr 2022
Cited by 7 | Viewed by 1874
Abstract
Inequalities play important roles not only in mathematics but also in other fields, such as economics and engineering. Even though many results are published as Hermite–Hadamard (H-H)-type inequalities, new researchers to these fields often find it difficult to understand them. Thus, some important [...] Read more.
Inequalities play important roles not only in mathematics but also in other fields, such as economics and engineering. Even though many results are published as Hermite–Hadamard (H-H)-type inequalities, new researchers to these fields often find it difficult to understand them. Thus, some important discoverers, such as the formulations of H-H-type inequalities of α-type real-valued convex functions, along with various classes of convexity through differentiable mappings and for fractional integrals, are presented. Some well-known examples from the previous literature are used as illustrations. In the many above-mentioned inequalities, the symmetrical behavior arises spontaneously. Full article
(This article belongs to the Special Issue Inequality and Symmetry in Mathematical Analysis)
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