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Axioms
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Analysis of Mathematical Inequalities
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Analysis of 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 2024) | Viewed by 5747

Special Issue Editor

Dr. Muhammad Bilal Khan

E-Mail
Guest Editor
Department of Mathematics and Computer Science, Transilvania University of Brasov, 29 Eroilor Boulevard, 500036 Brasov, Romania
Interests: soft set theory; fuzzy integral inequalities; fuzzy graph theory; fuzzy decision-making

Special Issue Information

Dear Colleagues,

The extraordinary theory of inequalities is a long-standing topic in many different mathematical areas. It remains an attractive research subject, with many interesting applications in fuzzy fractional calculus, fuzzy quantum calculus, operator theory, operator equations, network theory, and quantum information theory. At present, this is a very active research area that has been enriched by the interplay between individual areas.

The numerical integration and estimation of definite integrals is a vital piece of applied science. Simpson's rules are momentous among the numerical techniques.

This Special Issue will collate original research papers in all areas of mathematics and its numerous applications that are concerned with inequalities or their basic role. The research results presented are related to the improvement, extensions, and generalizations of classical and recent inequalities and highlight their applications in functional analysis, nonlinear functional analysis, multivariate analysis, quantum calculus, statistics, probability, and other relevant fields.

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

Dr. Muhammad Bilal Khan
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

  • fuzzy integral inequalities
  • generalized convexity
  • quantum calculus
  • fuzzy fractional calculus
  • interval-valued calculus
  • multivariate analysis
  • means
  • operator theory
  • approximation theory

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (5 papers)

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Research

22 pages, 344 KiB  
Article
New Improvements of the Jensen–Mercer Inequality for Strongly Convex Functions with Applications
by Muhammad Adil Khan, Slavica Ivelić Bradanović and Haitham Abbas Mahmoud
Axioms 2024, 13(8), 553; https://doi.org/10.3390/axioms13080553 - 14 Aug 2024
Viewed by 1135
Abstract
In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about [...] Read more.
In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of strongly convex functions, along with some previously known results about strongly convex functions. We are also focused on important applications of the derived results in information theory, deducing estimates for χ-divergence, Kullback–Leibler divergence, Hellinger distance, Bhattacharya distance, Jeffreys distance, and Jensen–Shannon divergence. Additionally, we prove some applications to Mercer-type power means at the end. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
31 pages, 431 KiB  
Article
Fuzzy Milne, Ostrowski, and Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin Convexity and Their Applications
by Juan Wang, Valer-Daniel Breaz, Yasser Salah Hamed, Luminita-Ioana Cotirla and Xuewu Zuo
Axioms 2024, 13(7), 465; https://doi.org/10.3390/axioms13070465 - 10 Jul 2024
Viewed by 764
Abstract
In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ-Godunova–Levin convex fuzzy number mappings, to [...] Read more.
In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ-Godunova–Levin convex fuzzy number mappings, to derive Ostrowski’s and Hermite–Hadamard-type inequalities for fuzzy number mappings. Using the fuzzy Kulisch–Miranker order, we also establish connections with Hermite–Hadamard-type inequalities. Furthermore, we explore novel ideas and results based on Hermite–Hadamard–Fejér and provide examples and applications to illustrate our findings. Some very interesting examples are also provided to discuss the validation of the main results. Additionally, some new exceptional and classical outcomes have been obtained, which can be considered as applications of our main results. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
17 pages, 1033 KiB  
Article
Some New Estimations of Ostrowski-Type Inequalities for Harmonic Fuzzy Number Convexity via Gamma, Beta and Hypergeometric Functions
by Azzh Saad Alshehry, Loredana Ciurdariu, Yaser Saber and Amal F. Soliman
Axioms 2024, 13(7), 455; https://doi.org/10.3390/axioms13070455 - 4 Jul 2024
Cited by 1 | Viewed by 754
Abstract
This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish [...] Read more.
This paper demonstrates several of Ostrowski-type inequalities for fuzzy number functions and investigates their connections with other inequalities. Specifically, employing the Aumann integral and the Kulisch–Miranker order, as well as the inclusion order on the space of real and compact intervals, we establish various Ostrowski-type inequalities for fuzzy-valued mappings (F·V·Ms). Furthermore, by employing diverse orders, we establish connections with the classical versions of Ostrowski-type inequalities. Additionally, we explore new ideas and results rooted in submodular measures, accompanied by examples and applications to illustrate our findings. Moreover, by using special functions, we have provided some applications of Ostrowski-type inequalities. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
25 pages, 399 KiB  
Article
A New Class of Coordinated Non-Convex Fuzzy-Number-Valued Mappings with Related Inequalities and Their Applications
by Aleksandr Rakhmangulov, A. F. Aljohani, Ali Mubaraki and Saad Althobaiti
Axioms 2024, 13(6), 404; https://doi.org/10.3390/axioms13060404 - 16 Jun 2024
Cited by 2 | Viewed by 1002
Abstract
Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on [...] Read more.
Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann’s integral theory, the Hermite–Hadamard’s type inequalities are introduced for a newly defined class of nonconvex functions, which is known as U·D preinvex fuzzy number-valued mappings (U·D preinvex F·N·V·Ms) on coordinates. Some Pachpatte-type inequalities are also established for the product of two U·D preinvex F·N·V·Ms, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann’s integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
20 pages, 2547 KiB  
Article
The Estimation of Different Kinds of Integral Inequalities for a Generalized Class of Convex Mapping and a Harmonic Set via Fuzzy Inclusion Relations and Their Applications in Quadrature Theory
by Ali Althobaiti, Saad Althobaiti and Miguel Vivas Cortez
Axioms 2024, 13(6), 344; https://doi.org/10.3390/axioms13060344 - 22 May 2024
Cited by 2 | Viewed by 1039
Abstract
The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings (F-N-V-Ms), [...] Read more.
The relationship between convexity and symmetry is widely recognized. In fuzzy theory, both concepts exhibit similar behavior. It is crucial to remember that real and interval-valued mappings are special instances of fuzzy-number-valued mappings (F-N-V-Ms), as fuzzy theory relies on the unit interval, which is crucial to resolving problems with interval analysis and fuzzy number theory. In this paper, a new harmonic convexities class of fuzzy numbers has been introduced via up and down relation. We show several Hermite–Hadamard (H⋅H) and Fejér-type inequalities by the implementation of fuzzy Aumann integrals using the newly defined class of convexities. Some nontrivial examples are also presented to validate the main outcomes. Full article
(This article belongs to the Special Issue Analysis of Mathematical Inequalities)
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