Special Issue "Functional Equations and Analytic Inequalities"

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

Deadline for manuscript submissions: closed (31 May 2021).

Special Issue Editor

Prof. Dr. Alina Alb Lupas
E-Mail Website
Guest 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
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Special Issue Information

Dear Colleagues,

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.

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. 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 papers will be 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 1800 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 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 (19 papers)

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Research

Article
Some Results of New Subclasses for Bi-Univalent Functions Using Quasi-Subordination
Symmetry 2021, 13(9), 1653; https://doi.org/10.3390/sym13091653 - 08 Sep 2021
Viewed by 322
Abstract
In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions [...] Read more.
In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a2 and a3 for functions of these subclasses. We discuss the improved results for the associated classes involving many of the new and well-known consequences. We notice that there is symmetry in the results obtained for the new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ, as there is a symmetry for the estimations of the coefficients a2 and a3 for all the subclasses defind in our this paper. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Applications of the q-Srivastava-Attiya Operator Involving a Certain Family of Bi-Univalent Functions Associated with the Horadam Polynomials
Symmetry 2021, 13(7), 1230; https://doi.org/10.3390/sym13071230 - 08 Jul 2021
Cited by 3 | Viewed by 391
Abstract
In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the [...] Read more.
In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit disk U, which are associated with the Bazilevič functions and the λ-pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family SWΣ(δ,γ,λ,s,t,q,r). Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function Φ(z,s,a) is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Some Bounds for the Complex Čebyšev Functional of Functions of Bounded Variation
Symmetry 2021, 13(6), 990; https://doi.org/10.3390/sym13060990 - 02 Jun 2021
Viewed by 532
Abstract
In this paper, we provide several bounds for the modulus of the complex Čebyšev functional. Applications to the trapezoid and mid-point inequalities, that are symmetric inequalities, are also provided. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
On Markov Moment Problem and Related Results
Symmetry 2021, 13(6), 986; https://doi.org/10.3390/sym13060986 - 01 Jun 2021
Cited by 2 | Viewed by 703
Abstract
We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued [...] Read more.
We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an Lν1 space, where ν is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
An Application of the Principle of Differential Subordination to Analytic Functions Involving Atangana–Baleanu Fractional Integral of Bessel Functions
Symmetry 2021, 13(6), 971; https://doi.org/10.3390/sym13060971 - 31 May 2021
Cited by 3 | Viewed by 549
Abstract
The aim of this paper is to establish certain subordination results for analytic functions involving Atangana–Baleanu fractional integral of Bessel functions. Studying subordination properties by using various types of operators is a technique that is widely used. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Fractional Weighted Ostrowski-Type Inequalities and Their Applications
Symmetry 2021, 13(6), 968; https://doi.org/10.3390/sym13060968 - 29 May 2021
Cited by 1 | Viewed by 840
Abstract
An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. [...] Read more.
An important area in the field of applied and pure mathematics is the integral inequality. As it is known, inequalities aim to develop different mathematical methods. Nowadays, we need to seek accurate inequalities for proving the existence and uniqueness of the mathematical methods. The concept of convexity plays a strong role in the field of inequalities due to the behavior of its definition and its properties. Furthermore, there is a strong correlation between convexity and symmetry concepts. Whichever one we work on, we can apply it to the other one due the strong correlation produced between them, especially in the last few years. In this study, by using a new identity, we establish some new fractional weighted Ostrowski-type inequalities for differentiable quasi-convex functions. Further, further results for functions with a bounded first derivative are given. Finally, in order to illustrate the efficiency of our main results, some applications to special means are obtain. The obtained results generalize and refine certain known results. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
New Geometric Constants in Banach Spaces Related to the Inscribed Equilateral Triangles of Unit Balls
Symmetry 2021, 13(6), 951; https://doi.org/10.3390/sym13060951 - 27 May 2021
Cited by 2 | Viewed by 659
Abstract
Geometric constant is one of the important tools to study geometric properties of Banach spaces. In this paper, we will introduce two new geometric constants JL(X) and YJ(X) in Banach spaces, which are symmetric and [...] Read more.
Geometric constant is one of the important tools to study geometric properties of Banach spaces. In this paper, we will introduce two new geometric constants JL(X) and YJ(X) in Banach spaces, which are symmetric and related to the side lengths of inscribed equilateral triangles of unit balls. The upper and lower bounds of JL(X) and YJ(X) as well as the values of JL(X) and YJ(X) for Hilbert spaces and some common Banach spaces will be calculated. In addition, some inequalities for JL(X), YJ(X) and some significant geometric constants will be presented. Furthermore, the sufficient conditions for uniformly non-square and normal structure, and the necessary conditions for uniformly non-square and uniformly convex will be established. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Asymptotic Properties of Solutions to Discrete Volterra Monotone Type Equations
Symmetry 2021, 13(6), 918; https://doi.org/10.3390/sym13060918 - 21 May 2021
Cited by 1 | Viewed by 409
Abstract
We investigate the higher order nonlinear discrete Volterra equations. We study solutions with prescribed asymptotic behavior. For example, we establish sufficient conditions for the existence of asymptotically polynomial, asymptotically periodic or asymptotically symmetric solutions. On the other hand, we are dealing with the [...] Read more.
We investigate the higher order nonlinear discrete Volterra equations. We study solutions with prescribed asymptotic behavior. For example, we establish sufficient conditions for the existence of asymptotically polynomial, asymptotically periodic or asymptotically symmetric solutions. On the other hand, we are dealing with the problem of approximation of solutions. Among others, we present conditions under which any bounded solution is asymptotically periodic. Using our techniques, based on the iterated remainder operator, we can control the degree of approximation. In this paper we choose a positive non-increasing sequence u and use o(un) as a measure of approximation. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities
Symmetry 2021, 13(5), 904; https://doi.org/10.3390/sym13050904 - 19 May 2021
Cited by 1 | Viewed by 503
Abstract
In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using [...] Read more.
In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using a,b,c, c0,1,2,. The study done in this paper extends the results on the univalence of the considered function taking a,b,c, with c0,1,2, two criteria being stated in the corollaries of the proved theorems. An interpretation of the univalence results from the sets inclusion view is also given, underlining the geometrical properties of the outcomes. Examples showing how the univalence results can be applied are also included. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order
Symmetry 2021, 13(5), 896; https://doi.org/10.3390/sym13050896 - 18 May 2021
Cited by 2 | Viewed by 516
Abstract
A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the existence of solutions. It leads [...] Read more.
A boundary value problem for Hadamard fractional differential equations of variable order is studied. Note the symmetry of a transformation of a system of differential equations is connected with the locally solvability which is the same as the existence of solutions. It leads to the necessity of obtaining existence criteria for a boundary value problem for Hadamard fractional differential equations of variable order. Also, the stability in the sense of Ulam–Hyers–Rassias is investigated. The results are obtained based on the Kuratowski measure of noncompactness. An example illustrates the validity of the observed results. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Invariant Solutions of Black–Scholes Equation with Ornstein–Uhlenbeck Process
Symmetry 2021, 13(5), 847; https://doi.org/10.3390/sym13050847 - 11 May 2021
Viewed by 481
Abstract
This paper analyses the model of Black–Scholes option pricing from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the Black–Scholes equation. Furthermore, corresponding determining equations were constructed and new symmetries [...] Read more.
This paper analyses the model of Black–Scholes option pricing from the point of view of the group theoretic approach. The study identified new independent variables that lead to the transformation of the Black–Scholes equation. Furthermore, corresponding determining equations were constructed and new symmetries were found. As a result, the findings of the study demonstrate of the integrability of the model to present an invariant solution for the Ornstein–Uhlenbeck stochastic process. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
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Article
New Hermite–Hadamard Inequalities in Fuzzy-Interval Fractional Calculus and Related Inequalities
Symmetry 2021, 13(4), 673; https://doi.org/10.3390/sym13040673 - 13 Apr 2021
Cited by 20 | Viewed by 542
Abstract
It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of [...] Read more.
It is a familiar fact that inequalities have become a very popular method using fractional integrals, and that this method has been the driving force behind many studies in recent years. Many forms of inequality have been studied, resulting in the introduction of new trend in inequality theory. The aim of this paper is to use a fuzzy order relation to introduce various types of inequalities. On the fuzzy interval space, this fuzzy order relation is defined level by level. With the help of this relation, firstly, we derive some discrete Jensen and Schur inequalities for convex fuzzy interval-valued functions (convex fuzzy-IVF), and then, we present Hermite–Hadamard inequalities (HH-inequalities) for convex fuzzy-IVF via fuzzy interval Riemann–Liouville fractional integrals. These outcomes are a generalization of a number of previously known results, and many new outcomes can be deduced as a result of appropriate parameter “γ” and real valued function “Ω” selections. We hope that our fuzzy order relations results can be used to evaluate a number of mathematical problems related to real-world applications. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte Fractional Inequalities
Symmetry 2021, 13(3), 463; https://doi.org/10.3390/sym13030463 - 12 Mar 2021
Viewed by 332
Abstract
Here we present Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and ψ-Hilfer fractional derivatives. All estimates are with respect to norms ·p, 1p. [...] Read more.
Here we present Hilfer-Polya, ψ-Hilfer Ostrowski and ψ-Hilfer-Hilbert-Pachpatte types fractional inequalities. They are univariate inequalities involving left and right Hilfer and ψ-Hilfer fractional derivatives. All estimates are with respect to norms ·p, 1p. At the end we provide applications. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
New Applications of the Fractional Integral on Analytic Functions
Symmetry 2021, 13(3), 423; https://doi.org/10.3390/sym13030423 - 05 Mar 2021
Cited by 2 | Viewed by 497
Abstract
The fractional integral is a function known for the elegant results obtained when introducing new operators; it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a [...] Read more.
The fractional integral is a function known for the elegant results obtained when introducing new operators; it has proved to have interesting applications. In the present paper, differential subordinations and superodinations for the fractional integral of the confluent hypergeometric function introduced in a previously published paper are presented. A sandwich-type theorem at the end of the original part of the paper connects the outcomes of the studies done using the dual theories. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
A Hilbert-Type Integral Inequality in the Whole Plane Related to the Arc Tangent Function
Symmetry 2021, 13(2), 351; https://doi.org/10.3390/sym13020351 - 21 Feb 2021
Viewed by 601
Abstract
In this work we establish a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of the arc tangent function. We prove that the constant factor, which is associated with the cosine function, is optimal. Some [...] Read more.
In this work we establish a few equivalent statements of a Hilbert-type integral inequality in the whole plane related to the kernel of the arc tangent function. We prove that the constant factor, which is associated with the cosine function, is optimal. Some special cases as well as some operator expressions are also presented. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Differential Subordination and Superordination Results Using Fractional Integral of Confluent Hypergeometric Function
Symmetry 2021, 13(2), 327; https://doi.org/10.3390/sym13020327 - 17 Feb 2021
Cited by 8 | Viewed by 836
Abstract
Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types [...] Read more.
Both the theory of differential subordination and its dual, the theory of differential superordination, introduced by Professors Miller and Mocanu are based on reinterpreting certain inequalities for real-valued functions for the case of complex-valued functions. Studying subordination and superordination properties using different types of operators is a technique that is still widely used, some studies resulting in sandwich-type theorems as is the case in the present paper. The fractional integral of confluent hypergeometric function is introduced in the paper and certain subordination and superordination results are stated in theorems and corollaries, the study being completed by the statement of a sandwich-type theorem connecting the results obtained by using the two theories. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
About the Cauchy–Bunyakovsky–Schwarz Inequality for Hilbert Space Operators
Symmetry 2021, 13(2), 305; https://doi.org/10.3390/sym13020305 - 11 Feb 2021
Viewed by 595
Abstract
The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear [...] Read more.
The symmetric shape of some inequalities between two sequences of real numbers generates inequalities of the same shape in operator theory. In this paper, we study a new refinement of the Cauchy–Bunyakovsky–Schwarz inequality for Euclidean spaces and several inequalities for two bounded linear operators on a Hilbert space, where we mention Bohr’s inequality and Bergström’s inequality for operators. We present an inequality of the Cauchy–Bunyakovsky–Schwarz type for bounded linear operators, by the technique of the monotony of a sequence. We also prove a refinement of the Aczél inequality for bounded linear operators on a Hilbert space. Finally, we present several applications of some identities for Hermitian operators. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function
Symmetry 2021, 13(2), 259; https://doi.org/10.3390/sym13020259 - 04 Feb 2021
Cited by 4 | Viewed by 508
Abstract
The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called [...] Read more.
The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory. Later, in 2003, a particular form of inequality in the complex plane was also defined by them as dual notion for subordination, the notion of differential superordination and with it, the theory of differential superordination appeared. In this paper, the theory of differential superordination is applied to confluent hypergeometric function. Hypergeometric functions are intensely studied nowadays, the interest on the applications of those functions in complex analysis being renewed by their use in the proof of Bieberbach’s conjecture given by de Branges in 1985. Using the theory of differential superodination, best subordinants of certain differential superordinations involving confluent (Kummer) hypergeometric function are stated in the theorems and relation with previously obtained results are highlighted in corollaries using particular functions and in a sandwich-type theorem. An example is also enclosed in order to show how the theoretical findings can be applied. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
Article
A Modified PRP-CG Type Derivative-Free Algorithm with Optimal Choices for Solving Large-Scale Nonlinear Symmetric Equations
Symmetry 2021, 13(2), 234; https://doi.org/10.3390/sym13020234 - 30 Jan 2021
Cited by 2 | Viewed by 617
Abstract
Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices for the modified Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) method by minimizing the measure function of the search direction matrix and combining the proposed direction with [...] Read more.
Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices for the modified Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) method by minimizing the measure function of the search direction matrix and combining the proposed direction with the default Newton direction. In addition, the corresponding PRP parameters are incorporated with the Li and Fukushima approximate gradient to propose two robust CG-type algorithms for finding solutions for large-scale systems of symmetric nonlinear equations. We have also demonstrated the global convergence of the suggested algorithms using some classical assumptions. Finally, we demonstrated the numerical advantages of the proposed algorithms compared to some of the existing methods for nonlinear symmetric equations. Full article
(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)
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