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Symmetry
Special Issues
Functional Equations and Inequalities in 2022
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Functional Equations and Inequalities in 2022

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 2068

Special Issue Editor

Prof. Dr. Roman Ger

E-Mail Website
Guest Editor
Institute of Mathematics, Silesian University of Katowice, Bankowa 12, 40-007 Katowice, Poland
Interests: existence and properties of solutions of various functional equations and inequalities in different function spaces under the weakest possible regularity conditions; conditional and alternative functional equations and inequalities; applications of methods of the theory of functional equations in dealing with some special problems from geometry, algebra, and functional analysis; measure theory and probability theory; Hyers-Ulam stability of functional equations and inequalities; characterization of mappings via functional equations; analogies between measure and category and their generalizations; theory of mean values; some special problems in the theory of functional equations in a single variable and iteration theory; convex analysis, in particular, theory of convex mappings and their generalizations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to submit papers related to various aspects of functional equations and inequalities and their applications, including (but not limited to) solution methods of functional equations on various classic as well as abstract structures, characterizations of different mappings and spaces, convex functions (functionals) and their generalizations, stability and functional equations postulated almost everywhere, Hahn–Banach type separation theory, sandwich theorems, theory of means, orthogonal additivity, difference property, alienation of functional equations, iterations (dynamical systems), iterative functional equations, multifunctions and functional inclusions, functional equations in fuzzy logic and fuzzy set theory, invariant means, and related topics.

Prof. Dr. Roman Ger
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. 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

  • functional equations
  • abstract structures
  • Hahn-Banach type separation theory
  • sandwich theorems
  • orthogonal additivity
  • alienation of functional equations
  • iterative functional equations
  • multifunctions and functional inclusions
  • fuzzy logic
  • fuzzy set theory

Published Papers (1 paper)

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Research

25 pages, 486 KiB  
Article
I.V-CR-γ-Convex Functions and Their Application in Fractional Hermite–Hadamard Inequalities
by Miguel Vivas-Cortez, Sofia Ramzan, Muhammad Uzair Awan, Muhammad Zakria Javed, Awais Gul Khan and Muhammad Aslam Noor
Symmetry 2023, 15(7), 1405; https://doi.org/10.3390/sym15071405 - 12 Jul 2023
Cited by 3 | Viewed by 1649
Abstract
In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. Interval-valued convex mappings are a special type of [...] Read more.
In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. Interval-valued convex mappings are a special type of set-valued maps. These have a close relationship with symmetry analysis. One of the important aspects of the relationship between convex and symmetric analysis is the ability to work on one field and apply its principles to another. In this paper, we introduce a novel class of interval-valued (I.V.) functions called CR-γ-convex functions based on a non-negative mapping γ and center-radius ordering relation. Due to its generic property, a set of new and known forms of convexity can be obtained. First, we derive new generalized discrete and integral forms of Jensen’s inequalities using CR-γ-convex I.V. functions. We employ this definition and Riemann-Liouville fractional operators to develop new fractional versions of Hermite-Hadamard’s, Hermite-Hadamard-Fejer, and Pachpatte’s type integral inequalities. We examine various key properties of this class of functions by considering them as special cases. Finally, we support our findings with interesting examples and graphical representations. Full article
(This article belongs to the Special Issue Functional Equations and Inequalities in 2022)
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