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Symmetry
Special Issues
Advance in Functional Equations, Second Edition
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Advance in Functional Equations, Second Edition

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 1381

Special Issue Editors

Dr. Włodzimierz Fechner

E-Mail Website
Guest Editor
Institute of Mathematics, Lodz University of Technology, al. Politechniki 8, 93-590 Łódź, Poland
Interests: functional equations; functional inequalities; fuzzy logic; Hyers-Ulam stability; classical analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Jacek Chudziak

E-Mail Website
Guest Editor
Department of Natural Sciences, Rzeszów University, Rzeszów, Poland
Interests: functional equations; functional inequalities; utility theory; decision making under risk
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Due to the great success of our Special Issue "Advance in Functional Equations" we decided to set up a second volume. 

It is our pleasure to invite you to contribute to the special issue of Symmetry dedicated to functional equations. Functional equations and inequalities find their applications in many areas of science, including approximate reasoning, physics, economy and behavioral sciences. Symmetry is a fundamental attribute of several functional equations, including the famous Cauchy functional equations. Free variables appearing in many equations often enjoy several symmetry properties and many techniques rely on exploring them. Therefore, functional equations and inequalities fit into the scope of the multidisciplinary journal Symmetry.

This issue is mainly devoted to research connected with functional equations and inequalities of one and several variables, their stability in a sense of Ulam and applications in all areas of science. In particular, we seek for submissions which bring new methods and new ideas to the field and which discover connections with various branches of science. Papers dealing with applications of functional equations or inequalities are also welcome.

Welcome to read the publications in "Advance in Functional Equations" at https://www.mdpi.com/journal/symmetry/special_issues/Advance_Functional_Equations.

Dr. Włodzimierz Fechner
Dr. Jacek Chudziak
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

  • functional equation
  • functional inequality
  • stability in a sense of Ulam
  • generalized Hyers–Ulam
  • stability of functional equation
  • hyperstability and superstability
  • applications of functional equations
  • applications of functional inequalities
  • utility theory
  • risk maeasures and their properties
  • symmetry in functional equations and inequalities

Related Special Issue

Published Papers (2 papers)

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Research

17 pages, 507 KiB  
Article
Comparative Analysis of Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation
by Ma’mon Abu Hammad, Rami Alkhateeb, Nabil Laiche, Adel Ouannas and Shameseddin Alshorm
Symmetry 2024, 16(5), 581; https://doi.org/10.3390/sym16050581 - 8 May 2024
Viewed by 367
Abstract
This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive [...] Read more.
This paper makes a significant contribution by focusing on estimating the coefficients of a sample of non-linear time series, a subject well-established in the statistical literature, using bilinear time series. Specifically, this study delves into a subset of bilinear models where Generalized Autoregressive Conditional Heteroscedastic (GARCH) models serve as the white noise component. The methodology involves applying the Klimko–Nilsen theorem, which plays a crucial role in extracting the asymptotic behavior of the estimators. In this context, the Generalized Autoregressive Conditional Heteroscedastic model of order (1,1) noted that the GARCH (1,1) model is defined as the white noise for the coefficients of the example models. Notably, this GARCH model satisfies the condition of having time-varying coefficients. This study meticulously outlines the essential stationarity conditions required for these models. The estimation of coefficients is accomplished by applying the least squares method. One of the key contributions lies in utilizing the fundamental theorem of Klimko and Nilsen, to prove the asymptotic behavior of the estimators, particularly how they vary with changes in the sample size. This paper illuminates the impact of estimators and their approximations based on varying sample sizes. Extending our study to include the estimation of bilinear models alongside GARCH and GARCH symmetric coefficients adds depth to our analysis and provides valuable insights into modeling financial time series data. Furthermore, this study sheds light on the influence of the GARCH white noise trace on the estimation of model coefficients. The results establish a clear connection between the model characteristics and the nature of the white noise, contributing to a more profound understanding of the relationship between these elements. Full article
(This article belongs to the Special Issue Advance in Functional Equations, Second Edition)
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14 pages, 270 KiB  
Article
A Functional Inequality and a New Class of Probabilities in the N-Person Red-and-Black Game
by Włodzimierz Fechner and Maria Słomian
Symmetry 2024, 16(3), 325; https://doi.org/10.3390/sym16030325 - 7 Mar 2024
Viewed by 628
Abstract
In this paper, we explore a model of an N-player, non-cooperative stochastic game, drawing inspiration from the discrete formulation of the red-and-black gambling problem, as initially introduced by Dubins and Savage in 1965. We extend upon the work of Pontiggia from 2007, [...] Read more.
In this paper, we explore a model of an N-player, non-cooperative stochastic game, drawing inspiration from the discrete formulation of the red-and-black gambling problem, as initially introduced by Dubins and Savage in 1965. We extend upon the work of Pontiggia from 2007, presenting a main theorem that broadens the conditions under which bold strategies by all players can achieve a Nash equilibrium. This is obtained through the introduction of a novel functional inequality, which serves as a key analytical tool in our study. This inequality enables us to circumvent the restrictive conditions of super-multiplicativity and super-additivity prevalent in the works of Pontiggia and others. We conclude this paper with a series of illustrative examples that demonstrate the efficacy of our approach, notably highlighting its ability to accommodate a broader spectrum of probability functions than previously recognized in the existing literature. Full article
(This article belongs to the Special Issue Advance in Functional Equations, Second Edition)
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