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14 pages, 577 KiB

Open AccessArticle

Applications of First-Order Differential Subordination for Subfamilies of Analytic Functions Related to Symmetric Image Domains

by Muhammad Ghaffar Khan, Bilal Khan, Jianhua Gong, Fairouz Tchier and Ferdous M. O. Tawfiq

Symmetry 2023, 15(11), 2004; https://doi.org/10.3390/sym15112004 - 31 Oct 2023

Cited by 2 | Viewed by 606

Abstract

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of [...] Read more.

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

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26 pages, 371 KiB

Open AccessArticle

New Monotonic Properties for Solutions of a Class of Functional Differential Equations and Their Applications

by Fahd Masood, Osama Moaaz, Ghada AlNemer and Hamdy El-Metwally

Symmetry 2023, 15(10), 1956; https://doi.org/10.3390/sym15101956 - 23 Oct 2023

Viewed by 1071

Abstract

This paper delves into the enhancement of asymptotic and oscillatory behaviors in solutions to even-order neutral differential equations with multiple delays. The main objective is to establish improved inequalities to advance the understanding of oscillation theory for these equations. The paper’s approach is [...] Read more.

This paper delves into the enhancement of asymptotic and oscillatory behaviors in solutions to even-order neutral differential equations with multiple delays. The main objective is to establish improved inequalities to advance the understanding of oscillation theory for these equations. The paper’s approach is centered on improving the understanding of the intricate relationship between solutions and their corresponding functions. This is achieved by harnessing the modified monotonic properties of positive solutions, which provide valuable insights into oscillation behavior. Furthermore, leveraging the symmetry between positive and negative solutions, we derived criteria that ensure oscillation for all solutions, with a specific emphasis on excluding only positive solutions. To illustrate the significance of our findings, we provide an illustrative example. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

11 pages, 468 KiB

Open AccessArticle

On Asymptotic Properties of Stochastic Neutral-Type Inertial Neural Networks with Mixed Delays

by Bingxian Wang, Honghui Yin and Bo Du

Symmetry 2023, 15(9), 1746; https://doi.org/10.3390/sym15091746 - 12 Sep 2023

Viewed by 504

Abstract

This article studies the stability problem of a class of stochastic neutral-type inertial delay neural networks. By introducing appropriate variable transformations, the second-order differential system is transformed into a first-order differential system. Using homeomorphism mapping, standard stochastic analyzing technology, the Lyapunov functional method [...] Read more.

This article studies the stability problem of a class of stochastic neutral-type inertial delay neural networks. By introducing appropriate variable transformations, the second-order differential system is transformed into a first-order differential system. Using homeomorphism mapping, standard stochastic analyzing technology, the Lyapunov functional method and the properties of a neutral operator, we establish new sufficient criteria for the unique existence and stochastically globally asymptotic stability of equilibrium points. An example is also provided, to show the validity of the established results. From our results, we find that, under appropriate conditions, random disturbances have no significant impact on the existence, stability, and symmetry of network systems. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

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9 pages, 262 KiB

Open AccessArticle

Infinitely Many Positive Solutions to Nonlinear First-Order Iterative Systems of Singular BVPs on Time Scales

by Famei Zheng, Xiaojing Wang, Xiwang Cheng and Bo Du

Symmetry 2023, 15(8), 1524; https://doi.org/10.3390/sym15081524 - 02 Aug 2023

Viewed by 484

Abstract

Iterative differential equations provide a new idea to study functional differential equations. The study of iterative equations can provide new methods for the study of differential equations with state-dependent delays. In this paper, we are concerned with proving the existence of infinitely many [...] Read more.

Iterative differential equations provide a new idea to study functional differential equations. The study of iterative equations can provide new methods for the study of differential equations with state-dependent delays. In this paper, we are concerned with proving the existence of infinitely many positive solutions to nonlinear first-order iterative systems of singular BVPs on time scales by using Krasnoselskii’s cone fixed point theorem in a Banach space. It is worth pointing out that in this paper, we can use the symmetry of the iterative process and Green’s function to transform the considered differential equation into an equivalent integral equation, which plays a key role in the proof of the theorem in this paper. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

19 pages, 392 KiB

Open AccessArticle

Symmetry and Asymmetry in Moment, Functional Equations, and Optimization Problems

by Octav Olteanu

Symmetry 2023, 15(7), 1471; https://doi.org/10.3390/sym15071471 - 24 Jul 2023

Cited by 3 | Viewed by 915

Abstract

The purpose of this work is to provide applications of real, complex, and functional analysis to moment, interpolation, functional equations, and optimization problems. Firstly, the existence of the unique solution for a two-dimensional full Markov moment problem is characterized on the upper half-plane. [...] Read more.

The purpose of this work is to provide applications of real, complex, and functional analysis to moment, interpolation, functional equations, and optimization problems. Firstly, the existence of the unique solution for a two-dimensional full Markov moment problem is characterized on the upper half-plane. The issue of the unknown form of nonnegative polynomials on

R \times R_{+}

in terms of sums of squares is solved using polynomial approximation by special nonnegative polynomials, which are expressible in terms of sums of squares. The main new element is the proof of Theorem 1, based only on measure theory and on a previous approximation-type result. Secondly, the previous construction of a polynomial solution is completed for an interpolation problem with a finite number of moment conditions, pointing out a method of determining the coefficients of the solution in terms of the given moments. Here, one uses methods of symmetric matrix theory. Thirdly, a functional equation having nontrivial solution (defined implicitly) and a consequence are discussed. Inequalities, the implicit function theorem, and elements of holomorphic functions theory are applied. Fourthly, the constrained optimization of the modulus of some elementary functions of one complex variable is studied. The primary aim of this work is to point out the importance of symmetry in the areas mentioned above. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

21 pages, 330 KiB

Open AccessArticle

Refinements of the Euclidean Operator Radius and Davis–Wielandt Radius-Type Inequalities

by Tareq Hamadneh, Mohammad W. Alomari, Isra Al-Shbeil, Hala Alaqad, Raed Hatamleh, Ahmed Salem Heilat and Abdallah Al-Husban

Symmetry 2023, 15(5), 1061; https://doi.org/10.3390/sym15051061 - 11 May 2023

Cited by 1 | Viewed by 1305

Abstract

This paper proves several new inequalities for the Euclidean operator radius, which refine some recent results. It is shown that the new results are much more accurate than the related, recently published results. Moreover, inequalities for both symmetric and non-symmetric Hilbert space operators [...] Read more.

This paper proves several new inequalities for the Euclidean operator radius, which refine some recent results. It is shown that the new results are much more accurate than the related, recently published results. Moreover, inequalities for both symmetric and non-symmetric Hilbert space operators are studied. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

14 pages, 308 KiB

Open AccessArticle

Some Refinements of the Tensorial Inequalities in Hilbert Spaces

by Vuk Stojiljković, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby and Stojan Radenović

Symmetry 2023, 15(4), 925; https://doi.org/10.3390/sym15040925 - 16 Apr 2023

Cited by 3 | Viewed by 891

Abstract

Hermite–Hadamard inequalities and their refinements have been investigated for a long period of time. In this paper, we obtained refinements of the Hermite–Hadamard inequality of tensorial type for the convex functions of self-adjoint operators in Hilbert spaces. The obtained inequalities generalize the previously [...] Read more.

Hermite–Hadamard inequalities and their refinements have been investigated for a long period of time. In this paper, we obtained refinements of the Hermite–Hadamard inequality of tensorial type for the convex functions of self-adjoint operators in Hilbert spaces. The obtained inequalities generalize the previously obtained inequalities by Dragomir. We also provide useful Lemmas which enabled us to obtain the results. The examples of the obtained inequalities for specific convex functions have been given in the example and consequences section. Symmetry in the upper and lower bounds can be seen in the last Theorem of the paper given, as the upper and lower bounds differ by a constant. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

11 pages, 531 KiB

Open AccessArticle

An Analytical Approach to Solve the Fractional Benney Equation Using the q-Homotopy Analysis Transform Method

by Rasool Shah, Yousuf Alkhezi and Khaled Alhamad

Symmetry 2023, 15(3), 669; https://doi.org/10.3390/sym15030669 - 07 Mar 2023

Cited by 10 | Viewed by 1019

Abstract

This paper introduces an analytical approach for solving the Benney equation using the q-homotopy analysis transform method. The Benney equation is a nonlinear partial differential equation that has applications in diverse areas of physics and engineering. The q-homotopy analysis transform method is a [...] Read more.

This paper introduces an analytical approach for solving the Benney equation using the q-homotopy analysis transform method. The Benney equation is a nonlinear partial differential equation that has applications in diverse areas of physics and engineering. The q-homotopy analysis transform method is a numerical technique that has been successfully employed to solve a broad range of nonlinear problems. By utilizing this method, we derive approximate analytical solutions for the Benney equation. The results demonstrate that this method is a powerful and effective tool for obtaining accurate solutions for the equation. The proposed method offers a valuable contribution to the existing literature on the behavior of the Benney equation and provides researchers with a useful tool for solving this equation in various applications. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

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20 pages, 4643 KiB

Open AccessArticle

Cooperative Multi-Objective Control of Heterogeneous Vehicle Platoons on Highway with Varying Slopes

by Weiwei Kong, Tianmao Cai, Yugong Luo, Xuetong Wang and Fachao Jiang

Symmetry 2022, 14(12), 2647; https://doi.org/10.3390/sym14122647 - 14 Dec 2022

Cited by 2 | Viewed by 1205

Abstract

Stability, vehicle safety, energy saving, and passenger comfort are the major objectives of vehicle platooning control. These objectives are coupled, interrelated, and even conflicting, so integrated optimization of multiple objectives is quite challenging. Particularly for heterogeneous platoons, the difficulties are intensified for the [...] Read more.

Stability, vehicle safety, energy saving, and passenger comfort are the major objectives of vehicle platooning control. These objectives are coupled, interrelated, and even conflicting, so integrated optimization of multiple objectives is quite challenging. Particularly for heterogeneous platoons, the difficulties are intensified for the differences in vehicle dynamics. In this paper, the concept of symmetry is utilized in the platooning control, that is, the design method of each vehicle’s controller is the same. For each controller, it is to solve the optimal solution of multi-objective collaborative optimization. The concept of asymmetry is meanwhile embodied in the parameter setting of each controller, for the vehicle heterogeneity. The contents of this study are as follows. First, a mathematical model is established, in which the differences in vehicle dynamic characteristics of heterogeneous platoon, road slope, and aerodynamics are all taken into account. Then, based on distributed nonlinear model predictive control (DNMPC) method, multi-objective control strategies are proposed for the leader and followers, cooperatively. Furthermore, a weight coefficient optimization method is presented, to further improve the platoon’s multi-objective synthesis performance. Finally, comparative experiments are carried out. Results demonstrate that, compared with the classic cruise control method of vehicle platoons, the proposed approach can reduce energy consumption by more than 5% and improve tracking performance on the premise of passenger comfort. Real-road experiments verify that the proposed control system can function effectively and satisfy the computational requirements in real applications. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

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12 pages, 296 KiB

Open AccessPerspective

From Optimal Control to Mean Field Optimal Transport via Stochastic Neural Networks

by Luca Di Persio and Matteo Garbelli

Symmetry 2023, 15(9), 1724; https://doi.org/10.3390/sym15091724 - 08 Sep 2023

Viewed by 890

Abstract

In this paper, we derive a unified perspective for Optimal Transport (OT) and Mean Field Control (MFC) theories to analyse the learning process for Neural Network algorithms in a high-dimensional framework. We consider a Mean Field Neural Network in the context of MFC [...] Read more.

In this paper, we derive a unified perspective for Optimal Transport (OT) and Mean Field Control (MFC) theories to analyse the learning process for Neural Network algorithms in a high-dimensional framework. We consider a Mean Field Neural Network in the context of MFC theory referring to the mean field formulation of OT theory that may allow the development of efficient algorithms in a high-dimensional framework while providing a powerful tool in the context of explainable Artificial Intelligence. Full article

(This article belongs to the Special Issue Symmetry in Mathematical Analysis and Functional Analysis II)

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