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Mathematics
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Advances in Differential Analysis and Functional Analysis
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Advances in Differential Analysis and Functional Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".

Deadline for manuscript submissions: 30 June 2025 | Viewed by 8865

Special Issue Editors

Prof. Dr. Kadriye Aydemir

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Arts and Science, Amasya University, Amasya 05100, Turkey
Interests: operator theory; boundary value problems; differential analysis and functional analysis; transmission problems
Prof. Dr. Oktay Sh. Mukhtarov

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Arts and Science, Gaziosmanpaşa University, Tokat 60250, Turkey
Interests: operator theory; boundary value problems; analysis and functional analysis; sobolev spaces; isomorphism and completeness

Special Issue Information

Dear Colleagues,

“Advance in Differential Analysis and Functional Analysis” is a Special Issue of the open access peer-reviewed journal Mathematics, and aims to publish recent developments in scientific disciplines in which Differential Analysis and Functional Analysis play a basic role. The journal publishes articles by scientists in multiple interdisciplinary fields.

Differential Analysis is an important tool in Mathematical Analysis and concerns parts of analysis in which differentiation, whether derivative or differential, plays a central role. Differential Analysis is widely used in mathematics itself, as well as in areas such as statistics, computing, electrical circuit analysis, dynamical systems, economics and biology.

The historical roots of Functional Analysis lie in the study of the spaces of functions and in the formulation of the properties of operator transformations between function spaces. This point of view has been particularly useful in the study of differential and integral operators. This area of mathematics has both an intrinsic beauty, which we hope to convey to the reader, and a vast number of applications in many fields of mathematics. These include the analysis of PDEs, differential topology and geometry, symplectic topology, quantum mechanics, probability theory, geometric group theory, dynamical systems, ergodic theory and approximation theory.

This Special Issue is not restricted to the following list and welcomes papers on any remarkable properties or applications in the field of Differential Analysis and Functional Analysis.

Prof. Dr. Kadriye Aydemir
Prof. Dr. Oktay Sh. Mukhtarov
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • new developments in Functional Analysis
  • significant applications of Functional Analysis, including in other areas of mathematics (including the analysis of PDEs, differential equations, boundary value problems, differential topology and geometry, symplectic topology, quantum mechanics, probability theory, geometric group theory, and dynamical systems and approximation theory)
  • contributions to important problems and challenges in Functional Analysis
  • best approximation problems in Banach spaces
  • iterative procedures for fixed points or best proximity points
  • nonlinear optimization and applications
  • representation theory
  • theory of abstract and functional spaces
  • theory of operators
  • spectral theory
  • theory of operator equations
  • solvability of fixed-point equations of nonlinear operators
  • differential analysis and in its applications to physics and other areas of natural science (including statistics, computing, electrical circuit analysis, dynamical systems, economics and biology)

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

Published Papers (6 papers)

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Research

7 pages, 204 KiB  
Article
Harmonic Synthesis on Group Extensions
by László Székelyhidi
Mathematics 2024, 12(19), 3013; https://doi.org/10.3390/math12193013 - 27 Sep 2024
Viewed by 688
Abstract
Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated by the exponential monomials in the space; in other [...] Read more.
Harmonic synthesis describes translation invariant linear spaces of continuous complex valued functions on locally compact abelian groups. The basic result due to L. Schwartz states that such spaces on the reals are topologically generated by the exponential monomials in the space; in other words, the locally compact abelian group of the reals is synthesizable. This result does not hold for continuous functions in several real variables, as was shown by D.I. Gurevich’s counterexamples. On the other hand, if two discrete abelian groups have this synthesizability property, then so does their direct sum, as well. In this paper, we show that if two locally compact abelian groups have this synthesizability property and at least one of them is discrete, then their direct sum is synthesizable. In fact, more generally, we show that any extension of a synthesizable locally compact abelian group by a synthesizable discrete abelian group is synthesizable. This is an important step toward the complete characterization of synthesizable locally compact abelian groups. Full article
(This article belongs to the Special Issue Advances in Differential Analysis and Functional Analysis)
10 pages, 270 KiB  
Article
On System of Root Vectors of Perturbed Regular Second-Order Differential Operator Not Possessing Basis Property
by Makhmud Sadybekov and Nurlan Imanbaev
Mathematics 2023, 11(20), 4364; https://doi.org/10.3390/math11204364 - 20 Oct 2023
Cited by 2 | Viewed by 966
Abstract
This article delves into the spectral problem associated with a multiple differentiation operator that features an integral perturbation of boundary conditions of one specific type, namely, regular but not strengthened regular. The integral perturbation is characterized by the function px, which [...] Read more.
This article delves into the spectral problem associated with a multiple differentiation operator that features an integral perturbation of boundary conditions of one specific type, namely, regular but not strengthened regular. The integral perturbation is characterized by the function px, which belongs to the space L20,1. The concept of problems involving integral perturbations of boundary conditions has been the subject of previous studies, and the spectral properties of such problems have been examined in various early papers. What sets the problem under consideration apart is that the system of eigenfunctions for the unperturbed problem (when px≡0) lacks the property of forming a basis. To address this, a characteristic determinant for the spectral problem has been constructed. It has been established that the set of functions px, for which the system of eigenfunctions of the perturbed problem does not constitute an unconditional basis in L20,1, is dense within the space L20,1. Furthermore, it has been demonstrated that the adjoint operator shares a similar structure. Full article
(This article belongs to the Special Issue Advances in Differential Analysis and Functional Analysis)
12 pages, 281 KiB  
Article
Solving System of Linear Equations Using Common Fixed Point Theorems in Bicomplex Valued Metric Spaces
by Amnah Essa Shammaky and Jamshaid Ahmad
Mathematics 2023, 11(20), 4333; https://doi.org/10.3390/math11204333 - 18 Oct 2023
Viewed by 1149
Abstract
The aim of the present research article is to solve the system of linear equations using common fixed point theorems in the context of bicomplex valued metric spaces. To obtain our main objective, we introduce generalized contractive conditions in bicomplex valued metric spaces [...] Read more.
The aim of the present research article is to solve the system of linear equations using common fixed point theorems in the context of bicomplex valued metric spaces. To obtain our main objective, we introduce generalized contractive conditions in bicomplex valued metric spaces and establish common fixed point theorems for self mappings. We also give a significant example to demonstrate the legitimacy of the given theorems. Full article
(This article belongs to the Special Issue Advances in Differential Analysis and Functional Analysis)
24 pages, 1320 KiB  
Article
Codimension-Two Bifurcations of a Simplified Discrete-Time SIR Model with Nonlinear Incidence and Recovery Rates
by Dongpo Hu, Xuexue Liu, Kun Li, Ming Liu and Xiao Yu
Mathematics 2023, 11(19), 4142; https://doi.org/10.3390/math11194142 - 30 Sep 2023
Cited by 1 | Viewed by 2024
Abstract
In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 [...] Read more.
In this paper, a simplified discrete-time SIR model with nonlinear incidence and recovery rates is discussed. Here, using the integral step size and the intervention level as control parameters, we mainly discuss three types of codimension-two bifurcations (fold-flip bifurcation, 1:3 resonance, and 1:4 resonance) of the simplified discrete-time SIR model in detail by bifurcation theory and numerical continuation techniques. Parameter conditions for the occurrence of codimension-two bifurcations are obtained by constructing the corresponding approximate normal form with translation and transformation of several parameters and variables. To further confirm the accuracy of our theoretical analysis, numerical simulations such as phase portraits, bifurcation diagrams, and maximum Lyapunov exponents diagrams are provided. In particular, the coexistence of bistability states is observed by giving local attraction basins diagrams of different fixed points under different integral step sizes. It is possible to more clearly illustrate the model’s complex dynamic behavior by combining theoretical analysis and numerical simulation. Full article
(This article belongs to the Special Issue Advances in Differential Analysis and Functional Analysis)
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16 pages, 1288 KiB  
Article
Dynamics and Solutions of Higher-Order Difference Equations
by Mensah Folly-Gbetoula
Mathematics 2023, 11(17), 3693; https://doi.org/10.3390/math11173693 - 28 Aug 2023
Cited by 1 | Viewed by 1198
Abstract
The invariance method, known as Lie analysis, consists of finding a group of transformations that leave a difference equation invariant. This powerful tool permits one to lower the order, linearize and more importantly, obtain analytical solutions of difference and differential equations. In this [...] Read more.
The invariance method, known as Lie analysis, consists of finding a group of transformations that leave a difference equation invariant. This powerful tool permits one to lower the order, linearize and more importantly, obtain analytical solutions of difference and differential equations. In this study, we obtain the solutions and periodic solutions for some family of difference equations. We achieve this by performing an invariance analysis of this family. Eventually, symmetries are derived and used to construct canonical coordinates required for the derivation of the solutions. Moreover, periodic aspects of these solutions and the stability character of the equilibrium points are investigated. Full article
(This article belongs to the Special Issue Advances in Differential Analysis and Functional Analysis)
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18 pages, 309 KiB  
Article
Analytical Contribution to a Cubic Functional Integral Equation with Feedback Control on the Real Half Axis
by Ahmed M. A. El-Sayed, Hind H. G. Hashem and Shorouk M. Al-Issa
Mathematics 2023, 11(5), 1133; https://doi.org/10.3390/math11051133 - 24 Feb 2023
Cited by 4 | Viewed by 1540
Abstract
Synthetic biology involves trying to create new approaches using design-based approaches. A controller is a biological system intended to regulate the performance of other biological processes. The design of such controllers can be based on the results of control theory, including strategies. Integrated [...] Read more.
Synthetic biology involves trying to create new approaches using design-based approaches. A controller is a biological system intended to regulate the performance of other biological processes. The design of such controllers can be based on the results of control theory, including strategies. Integrated feedback control is central to regulation, sensory adaptation, and long-term effects. In this work, we present a study of a cubic functional integral equation with a general and new constraint that may help in investigating some real problems. We discuss the existence of solutions for an equation that involves a control variable in the class of bounded continuous functions BC(R+), by applying the technique of measure of noncompactness on R+. Furthermore, we establish sufficient conditions for the continuous dependence of the state function on the control variable. Finally, some remarks and discussion are presented to demonstrate our results. Full article
(This article belongs to the Special Issue Advances in Differential Analysis and Functional Analysis)
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