Symmetry in Functional Equations and Analytic Inequalities III

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

Deadline for manuscript submissions: closed (30 June 2023) | Viewed by 18604

Special Issue Editor

Department of Mathematics and Computer Science, Faculty of Informatics and Sciences, University of Oradea, Universitatii Street, 410087 Oradea, Romania
Interests: topological algebra; geometric function theory; inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issues “Functional Equations and Analytic Inequalities” and "Functional Equations and Analytic Inequalities II" saw considerable success, so we decided to reopen this Special Issue with the name "Functional Equations and Analytic Inequalities III". In this way, we still have privilege to publish high-quality papers.

The field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering.

Inequalities play a significant role in all fields of mathematics and present a very active and attractive field of research.

Symmetry properties of functions used in defining an equation or inequality could be studied in order to determine solutions with particular properties. As far as inequalities are concerned, the study of special functions, such as hypergeometric functions and special polynomials, considers their symmetry properties which could provide an interesting outcome. Studies on symmetry properties for different type of operators associated with the concept of quantum calculus could also be investigated.

This Special Issue promotes an exchange of ideas between eminent mathematicians from many parts of the world, dedicated to the functional equations and analytic inequalities. It is intended to boost cooperation among mathematicians working on a broad variety of pure and applied mathematical areas.

This volume of ideas and mathematical methods will include a wide area of applications in which the equations, inequalities, and computational techniques relevant to their solutions play an important role. These ideas and methods have a significant effect on everyday life, as new tools have been developed and achieved revolutionary research results, bringing scientists even closer to exact sciences, encouraging the emergence of new approaches, techniques, and perspectives in functional equations, analytical inequalities, etc. Please note that all submitted papers should be within the scope of the journal.

Prof. Dr. Alina Alb Lupas
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

  • symmetry
  • functional equations in several variables
  • difference equations
  • stability problems
  • set-valued functional equations
  • iterative functional equations and iteration theory
  • chaos
  • dynamical systems
  • iterative roots
  • iteration groups and semigroups
  • functional inequalities
  • convexity
  • inclusions for multivalued functions
  • differential and difference inequalities
  • means
  • applications in ODEs
  • PDEs
  • functional analysis
  • operator theory
  • approximation theory
  • number theory
  • actuarial mathematics
  • social sciences and others

Published Papers (15 papers)

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Research

11 pages, 356 KiB  
Article
A Modified Parallel Algorithm for a Common Fixed-Point Problem with Application to Signal Recovery
by Anchalee Khemphet, Raweerote Suparatulatorn, Pariwate Varnakovida and Phakdi Charoensawan
Symmetry 2023, 15(7), 1464; https://doi.org/10.3390/sym15071464 - 24 Jul 2023
Viewed by 649
Abstract
In this work, an algorithm is introduced for the problem of finding a common fixed point of a finite family of G-nonexpansive mappings in a real Hilbert space endowed with a directed graph G. This algorithm is a modified parallel algorithm [...] Read more.
In this work, an algorithm is introduced for the problem of finding a common fixed point of a finite family of G-nonexpansive mappings in a real Hilbert space endowed with a directed graph G. This algorithm is a modified parallel algorithm inspired by the inertial method and the Mann iteration process. Moreover, both weak and strong convergence theorems are provided for the algorithm. Furthermore, an application of the algorithm to a signal recovery problem with multiple blurring filters is presented. Consequently, the numerical experiment shows better results compared with the previous algorithm. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
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11 pages, 262 KiB  
Article
Fixed Points and λ-Weak Contractions
by Laura Manolescu and Adina Juratoni
Symmetry 2023, 15(7), 1442; https://doi.org/10.3390/sym15071442 - 18 Jul 2023
Viewed by 652
Abstract
In this paper, we introduce a new type of contractions on a metric space (X,d) in which the distance d(x,y) is replaced with a function, depending on a parameter λ, that is not [...] Read more.
In this paper, we introduce a new type of contractions on a metric space (X,d) in which the distance d(x,y) is replaced with a function, depending on a parameter λ, that is not symmetric in general. This function generalizes the usual case when λ=1/2 and can take bigger values than m1/2. We call these new types of contractions λ-weak contractions and we provide some of their properties. Moreover, we investigate cases when these contractions are Picard operators. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
16 pages, 322 KiB  
Article
Problems Concerning Coefficients of Symmetric Starlike Functions Connected with the Sigmoid Function
by Muhammad Imran Faisal, Isra Al-Shbeil, Muhammad Abbas, Muhammad Arif and Reem K. Alhefthi
Symmetry 2023, 15(7), 1292; https://doi.org/10.3390/sym15071292 - 21 Jun 2023
Cited by 3 | Viewed by 827
Abstract
In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of conformal maps. The primary goal of this paper [...] Read more.
In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of conformal maps. The primary goal of this paper was to calculate the sharp estimates of the initial coefficients and some of their combinations (the Hankel determinants, Zalcman’s functional, etc.) for the class of symmetric starlike functions linked with the sigmoid function. Moreover, we also determined the bounds of second-order Hankel determinants containing coefficients of logarithmic and inverse functions of the same class. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
21 pages, 463 KiB  
Article
Generalized AB-Fractional Operator Inclusions of Hermite–Hadamard’s Type via Fractional Integration
by Bandar Bin-Mohsin, Muhammad Uzair Awan, Muhammad Zakria Javed, Awais Gul Khan, Hüseyin Budak, Marcela V. Mihai and Muhammad Aslam Noor
Symmetry 2023, 15(5), 1012; https://doi.org/10.3390/sym15051012 - 01 May 2023
Cited by 3 | Viewed by 2375
Abstract
The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function [...] Read more.
The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function Eμ,α,lγ,δ,k,c(τ;p) as a kernel in the interval domain. Additionally, a new form of Atangana–Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in Eμ,α,lγ,δ,k,c(τ;p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite–Hadamard, Pachapatte, and Hermite–Hadamard–Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
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12 pages, 308 KiB  
Article
Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions
by Abdel Fatah Azzam, Shujaat Ali Shah, Alhanouf Alburaikan and Sheza M. El-Deeb
Symmetry 2023, 15(2), 509; https://doi.org/10.3390/sym15020509 - 14 Feb 2023
Cited by 5 | Viewed by 968
Abstract
Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect [...] Read more.
Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
14 pages, 288 KiB  
Article
Subordination Results for the Second-Order Differential Polynomials of Meromorphic Functions
by Sarah Ahmed, Maslina Darus and Georgia Irina Oros
Symmetry 2022, 14(12), 2587; https://doi.org/10.3390/sym14122587 - 07 Dec 2022
Viewed by 669
Abstract
The outcome of the research presented in this paper is the definition and investigation of two new subclasses of meromorphic functions. The new subclasses are introduced using a differential operator defined considering second-order differential polynomials of meromorphic functions in [...] Read more.
The outcome of the research presented in this paper is the definition and investigation of two new subclasses of meromorphic functions. The new subclasses are introduced using a differential operator defined considering second-order differential polynomials of meromorphic functions in U\{0}=zC:0<z<1. The investigation of the two new subclasses leads to establishing inclusion relations and the proof of convexity and convolution properties regarding each of the two subclasses. Further, involving the concept of subordination, the Fekete–Szegö problem is also discussed for the aforementioned subclasses. Symmetry properties derive from the use of the convolution and from the convexity proved for the new subclasses of functions. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
13 pages, 285 KiB  
Article
Symmetric Functional Set-Valued Integral Equations and Bihari–LaSalle Inequality
by Marek T. Malinowski
Symmetry 2022, 14(11), 2246; https://doi.org/10.3390/sym14112246 - 26 Oct 2022
Viewed by 795
Abstract
In the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more general than the standard Lipschitz condition, which allow the application [...] Read more.
In the paper, we consider functional set-valued integral equations whose representation contains set-valued integrals occurring symmetrically on both sides of the equation. On the coefficients of the equation, we impose certain conditions, more general than the standard Lipschitz condition, which allow the application of the Bihari–LaSalle inequality in the proofs of the obtained theorems. In this way, we obtain a result about the existence and uniqueness of the solution of the equation under consideration and the insensitivity of the solution in the case of minor changes in the parameters of the equation. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
12 pages, 254 KiB  
Article
Lie Symmetry Analysis of a Nonlinear System Characterizing Endemic Malaria
by Maba Boniface Matadi
Symmetry 2022, 14(11), 2240; https://doi.org/10.3390/sym14112240 - 25 Oct 2022
Viewed by 768
Abstract
In this paper, the integrability of a nonlinear system developing endemic Malaria was demonstrated using Prelle–Singer techniques. In addition, Lie symmetry techniques were employed to identify additional independent variables that led to the modification of the nonlinear model and the development of analytical [...] Read more.
In this paper, the integrability of a nonlinear system developing endemic Malaria was demonstrated using Prelle–Singer techniques. In addition, Lie symmetry techniques were employed to identify additional independent variables that led to the modification of the nonlinear model and the development of analytical solutions. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
12 pages, 288 KiB  
Article
Fixed-Point Theorems in Fuzzy Normed Linear Spaces for Contractive Mappings with Applications to Dynamic-Programming
by Tudor Bînzar, Flavius Pater and Sorin Nădăban
Symmetry 2022, 14(10), 1966; https://doi.org/10.3390/sym14101966 - 20 Sep 2022
Cited by 2 | Viewed by 1116
Abstract
The aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy [...] Read more.
The aim of this paper is to provide new ways of dealing with dynamic programming using a context of newly proven results about fixed-point problems in linear spaces endowed with a fuzzy norm. In our paper, the general framework is set to fuzzy normed linear spaces as they are defined by Nădăban and Dzitac. When completeness is required, we will use the George and Veeramani (G-V) setup, which, for our purposes, we consider to be more suitable than Grabiec-completeness. As an important result of our work, we give an original proof for a version of Banach’s fixed-point principle on this particular setup of fuzzy normed spaces, a variant of Jungck’s fixed-point theorem in the same setup, and they are proved in G-V-complete fuzzy normed spaces, paving the way for future developments in various fields within this framework, where our application of dynamic programming makes a proper example. As the uniqueness of almost every dynamic programming problem is necessary, the fixed-point theorems represent an important tool in achieving that goal. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
23 pages, 344 KiB  
Article
Some Hermite–Hadamard and Hermite–Hadamard–Fejér Type Fractional Inclusions Pertaining to Different Kinds of Generalized Preinvexities
by Muhammad Tariq, Soubhagya Kumar Sahoo, Sotiris K. Ntouyas, Omar Mutab Alsalami, Asif Ali Shaikh and Kamsing Nonlaopon
Symmetry 2022, 14(10), 1957; https://doi.org/10.3390/sym14101957 - 20 Sep 2022
Cited by 4 | Viewed by 1138
Abstract
Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction of new fractional operators has prompted another direction in different branches of mathematics and applied sciences. First, we investigate and prove new fractional equality. Considering this [...] Read more.
Fractional derivative and integral operators are often employed to present new generalizations of mathematical inequalities. The introduction of new fractional operators has prompted another direction in different branches of mathematics and applied sciences. First, we investigate and prove new fractional equality. Considering this equality as the auxiliary result, we attain some estimations of a Hermite–Hadamard type inequality involving s-preinvex, s-Godunova–Levin preinvex, and prequasi invex functions. In addition, we investigate a fractional order Hadamard–Fejér inequality and some of its refinements pertaining to h-preinvexity via a non-conformable fractional integral operator. Finally, we present a Pachpatte type inequality for the product of two preinvex functions. The findings as well as the special cases presented in this research are new and applications of our main results. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
14 pages, 326 KiB  
Article
Some New Fractional Integral Inequalities Pertaining to Generalized Fractional Integral Operator
by Omar Mutab Alsalami, Soubhagya Kumar Sahoo, Muhammad Tariq, Asif Ali Shaikh, Clemente Cesarano and Kamsing Nonlaopon
Symmetry 2022, 14(8), 1691; https://doi.org/10.3390/sym14081691 - 15 Aug 2022
Cited by 3 | Viewed by 1087
Abstract
Integral inequalities make up a comprehensive and prolific field of research within the field of mathematical interpretations. Integral inequalities in association with convexity have a strong relationship with symmetry. Different disciplines of mathematics and applied sciences have taken a new path as a [...] Read more.
Integral inequalities make up a comprehensive and prolific field of research within the field of mathematical interpretations. Integral inequalities in association with convexity have a strong relationship with symmetry. Different disciplines of mathematics and applied sciences have taken a new path as a result of the development of new fractional operators. Different new fractional operators have been used to improve some mathematical inequalities and to bring new ideas in recent years. To take steps forward, we prove various Grüss-type and Chebyshev-type inequalities for integrable functions in the frame of non-conformable fractional integral operators. The key results are proven using definitions of the fractional integrals, well-known classical inequalities, and classical relations. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
13 pages, 277 KiB  
Article
Bi-Univalent Problems Involving Certain New Subclasses of Generalized Multiplier Transform on Analytic Functions Associated with Modified Sigmoid Function
by Jamiu Olusegun Hamzat, Abiodun Tinuoye Oladipo and Georgia Irina Oros
Symmetry 2022, 14(7), 1479; https://doi.org/10.3390/sym14071479 - 19 Jul 2022
Cited by 4 | Viewed by 1065
Abstract
The object of the present work is to investigate certain new classes of bi-univalent functions introduced in this paper using the concept of subordination. The research involves a generalized multiplier transform defined in this paper which is a generalization of known operators and [...] Read more.
The object of the present work is to investigate certain new classes of bi-univalent functions introduced in this paper using the concept of subordination. The research involves a generalized multiplier transform defined in this paper which is a generalization of known operators and the modified sigmoid function. The results contained in the proved theorems refer to coefficient estimates for the functions in the newly introduced classes. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
20 pages, 945 KiB  
Article
Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application
by Jamilu Sabi’u, Kazeem Olalekan Aremu, Ali Althobaiti and Abdullah Shah
Symmetry 2022, 14(5), 936; https://doi.org/10.3390/sym14050936 - 05 May 2022
Cited by 4 | Viewed by 1563
Abstract
In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for [...] Read more.
In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
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19 pages, 1326 KiB  
Article
A Stochastic Discrete Empirical Interpolation Approach for Parameterized Systems
by Daheng Cai, Chengbin Yao and Qifeng Liao
Symmetry 2022, 14(3), 556; https://doi.org/10.3390/sym14030556 - 10 Mar 2022
Cited by 1 | Viewed by 1446
Abstract
As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis functions are generated through a random sampling procedure, [...] Read more.
As efficient separation of variables plays a central role in model reduction for nonlinear and nonaffine parameterized systems, we propose a stochastic discrete empirical interpolation method (SDEIM) for this purpose. In our SDEIM, candidate basis functions are generated through a random sampling procedure, and the dimension of the approximation space is systematically determined by a probability threshold. This random sampling procedure avoids large candidate sample sets for high-dimensional parameters, and the probability based stopping criterion can efficiently control the dimension of the approximation space. Numerical experiments are conducted to demonstrate the computational efficiency of SDEIM, which include separation of variables for general nonlinear functions, e.g., exponential functions of the Karhu nen–Loève (KL) expansion, and constructing reduced order models for FitzHugh–Nagumo equations, where symmetry among limit cycles is well captured by SDEIM. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
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12 pages, 1169 KiB  
Article
New Results on Fourth-Order Differential Subordination and Superordination for Univalent Analytic Functions Involving a Linear Operator
by Bassim Kareem Mihsin, Waggas Galib Atshan, Shatha S. Alhily and Alina Alb Lupaş
Symmetry 2022, 14(2), 324; https://doi.org/10.3390/sym14020324 - 05 Feb 2022
Cited by 9 | Viewed by 1368
Abstract
We present several new results for fourth-order differential subordination and superordination in this paper by using the differential linear operator Γπ,ρ,β,μfz. Relevant connections between the new results presented here and those considered in [...] Read more.
We present several new results for fourth-order differential subordination and superordination in this paper by using the differential linear operator Γπ,ρ,β,μfz. Relevant connections between the new results presented here and those considered in previous works are addressed. The properties and results concerning the differential subordination theory are symmetric to the properties obtained using the differential superordination theory, and by combining them, sandwich-type theorems are obtained. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)
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