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Topological Degree via a Degree of Nondensifiability and Applications 通过不可知度的拓扑度及其应用
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070482
N. Ouahab, J. J. Nieto, A. Ouahab
{"title":"Topological Degree via a Degree of Nondensifiability and Applications","authors":"N. Ouahab, J. J. Nieto, A. Ouahab","doi":"10.3390/axioms13070482","DOIUrl":"https://doi.org/10.3390/axioms13070482","url":null,"abstract":"The goal of this work is to introduce the notion of topological degree via the principle of the degree of nondensifiability (DND for short). We establish some new fixed point theorems, concerning, Schaefer’s fixed point theorem and the nonlinear alternative of Leray–Schauder type. As applications, we study the existence of mild solution of functional semilinear integro-differential equations.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 15","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141825369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Statistical and Direct Approximation Properties for a New Form of the Generalization of q-Bernstein Operators with the Parameter λ 带参数 λ 的 q-Bernstein 算子广义化新形式的一些统计和直接逼近特性
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070485
Lian-Ta Su, Esma Kangal, Ülkü Dinlemez Kantar, Qingbo Cai
{"title":"Some Statistical and Direct Approximation Properties for a New Form of the Generalization of q-Bernstein Operators with the Parameter λ","authors":"Lian-Ta Su, Esma Kangal, Ülkü Dinlemez Kantar, Qingbo Cai","doi":"10.3390/axioms13070485","DOIUrl":"https://doi.org/10.3390/axioms13070485","url":null,"abstract":"In this study, a different generalization of q-Bernstein operators with the parameter λ∈[−1,1] is created. The moments and central moments of these operators are calculated, a statistical approximation result for this new type of (λ,q)-Bernstein operators is obtained, and the convergence properties are analyzed using the Peetre K-functional and the modulus of continuity for this new operator. Finally, a numerical example is given to illustrate the convergence behavior of the newly defined operators.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 68","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141825301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fractional Sequential Coupled Systems of Hilfer and Caputo Integro-Differential Equations with Non-Separated Boundary Conditions 具有非分离边界条件的 Hilfer 和 Caputo 积分微分方程的分数序列耦合系统
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070484
A. Samadi, Sotiris K. Ntouyas, J. Tariboon
{"title":"Fractional Sequential Coupled Systems of Hilfer and Caputo Integro-Differential Equations with Non-Separated Boundary Conditions","authors":"A. Samadi, Sotiris K. Ntouyas, J. Tariboon","doi":"10.3390/axioms13070484","DOIUrl":"https://doi.org/10.3390/axioms13070484","url":null,"abstract":"In studying boundary value problems and coupled systems of fractional order in (1,2], involving Hilfer fractional derivative operators, a zero initial condition is necessary. The consequence of this fact is that boundary value problems and coupled systems of fractional order with non-zero initial conditions cannot be studied. For example, such boundary value problems and coupled systems of fractional order are those including separated, non-separated, or periodic boundary conditions. In this paper, we propose a method for studying a coupled system of fractional order in (1,2], involving fractional derivative operators of Hilfer and Caputo with non-separated boundary conditions. More precisely, a sequential coupled system of fractional differential equations including Hilfer and Caputo fractional derivative operators and non-separated boundary conditions is studied in the present paper. As explained in the concluding section, the opposite combination of Caputo and Hilfer fractional derivative operators requires zero initial conditions. By using Banach’s fixed point theorem, the uniqueness of the solution is established, while by applying the Leray–Schauder alternative, the existence of solution is obtained. Numerical examples are constructed illustrating the main results.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 19","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141824652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integrable Couplings and Two-Dimensional Unital Algebras 可积分耦合与二维单子代数
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070481
Wen-Xiu Ma
{"title":"Integrable Couplings and Two-Dimensional Unital Algebras","authors":"Wen-Xiu Ma","doi":"10.3390/axioms13070481","DOIUrl":"https://doi.org/10.3390/axioms13070481","url":null,"abstract":"The paper aims to demonstrate that a linear expansion in a unital two-dimensional algebra can generate integrable couplings, proposing a novel approach for their construction. The integrable couplings presented encompass a range of perturbation equations and nonlinear integrable couplings. Their corresponding Lax pairs and hereditary recursion operators are explicitly detailed. Concrete applications to the KdV equation and the AKNS system of nonlinear Schrödinger equations are extensively explored.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141824704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability Results for Some Classes of Cubic Functional Equations 几类三次函数方程的稳定性结果
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070480
El-sayed El-hady, Y. Sayyari, Mehdi Dehghanian, Y. Alruwaily
{"title":"Stability Results for Some Classes of Cubic Functional Equations","authors":"El-sayed El-hady, Y. Sayyari, Mehdi Dehghanian, Y. Alruwaily","doi":"10.3390/axioms13070480","DOIUrl":"https://doi.org/10.3390/axioms13070480","url":null,"abstract":"Applications involving functional equations (FUEQs) are commonplace. They are essential to various applications, such as fog computing. Ulam’s notion of stability is highly helpful since it provides a range of estimates between exact and approximate solutions. Using Brzdȩk’s fixed point technique (FPT), we establish the stability of the following cubic type functional equations (CFUEQs): Fξ13+ξ233+Fξ13−ξ233=2F(ξ1)+2F(ξ2),2Fξ13+ξ2323=F(ξ1)+F(ξ2) for all ξ1,ξ2∈R.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 97","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141825175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stability Analysis of a Credit Risk Contagion Model with Distributed Delay 具有分布式延迟的信用风险传染模型的稳定性分析
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070483
Martin Anokye, Luca Guerrini, A. L. Sackitey, Samuel E. Assabil, Henry Amankwah
{"title":"Stability Analysis of a Credit Risk Contagion Model with Distributed Delay","authors":"Martin Anokye, Luca Guerrini, A. L. Sackitey, Samuel E. Assabil, Henry Amankwah","doi":"10.3390/axioms13070483","DOIUrl":"https://doi.org/10.3390/axioms13070483","url":null,"abstract":"This research investigates the stability and occurrence of Hopf bifurcation in a credit risk contagion model, which includes distributed delay, using the chain trick method. The model is a generalized version of those previously examined. The model is an expanded version of those previously studied. Comparative analysis showed that unlike earlier models, which only used the nonlinear resistance coefficient to determine the rate of credit risk infection, the credit risk contagion rate is also affected by the weight given to past behaviors of credit risk participants. Therefore, it is recommended to model the transmission of credit risk contagion using dispersed delays.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 86","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141824815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Note on the Multiplicity of the Distinguished Points 区分点的多重性说明
Axioms Pub Date : 2024-07-18 DOI: 10.3390/axioms13070479
Weiping Li, Xiaoshen Wang
{"title":"A Note on the Multiplicity of the Distinguished Points","authors":"Weiping Li, Xiaoshen Wang","doi":"10.3390/axioms13070479","DOIUrl":"https://doi.org/10.3390/axioms13070479","url":null,"abstract":"Let P(x) be a system of polynomials in s variables, where x∈Cs. If z0 is an isolated zero of P, then the multiplicity and its structure at z0 can be revealed by the normal set of the quotient ring R() or its dual space R* or by certain numerical methods. In his book titled “Numerical Polynomial Algebra”, Stetter described the so-called distinguished points, which are embedded in a zero manifold of P, and the author defined their multiplicities. In this note, we will generalize the definition of distinguished points and give a more appropriate definition for their multiplicity, as well as show how to calculate the multiplicity of these points.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 65","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141825209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle 论顶点位于三角形支撑边上的等边三角形的一些性质
Axioms Pub Date : 2024-07-17 DOI: 10.3390/axioms13070478
D. Andrica, O. Bagdasar
{"title":"On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle","authors":"D. Andrica, O. Bagdasar","doi":"10.3390/axioms13070478","DOIUrl":"https://doi.org/10.3390/axioms13070478","url":null,"abstract":"The possible positions of an equilateral triangle whose vertices are located on the support sides of a generic triangle are studied. Using complex coordinates, we show that there are infinitely many such configurations, then we prove that the centroids of these equilateral triangles are collinear, defining two lines perpendicular to the Euler’s line of the original triangle. Finally, we obtain the complex coordinates of the intersection points and study some particular cases.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 46","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141831208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Potential Vector Fields of Soliton-Type Equations 论孤子型方程的势向量场
Axioms Pub Date : 2024-07-16 DOI: 10.3390/axioms13070476
A. Blaga
{"title":"On the Potential Vector Fields of Soliton-Type Equations","authors":"A. Blaga","doi":"10.3390/axioms13070476","DOIUrl":"https://doi.org/10.3390/axioms13070476","url":null,"abstract":"We highlight some properties of a class of distinguished vector fields associated to a (1,1)-tensor field and to an affine connection on a Riemannian manifold, with a special view towards the Ricci vector fields, and we characterize them with respect to statistical, almost Kähler, and locally product structures. In particular, we provide conditions for these vector fields to be closed, Killing, parallel, or semi-torse forming. In the gradient case, we give a characterization of the Euclidean sphere. Among these vector fields, the Ricci and torse-forming-like vector fields are particular cases.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141831989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations 运用数图和比较函数的非线性收缩，以及对奇异分微分方程的应用
Axioms Pub Date : 2024-07-16 DOI: 10.3390/axioms13070477
D. Filali, M. Dilshad, M. Akram
{"title":"Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations","authors":"D. Filali, M. Dilshad, M. Akram","doi":"10.3390/axioms13070477","DOIUrl":"https://doi.org/10.3390/axioms13070477","url":null,"abstract":"After the initiation of Jachymski’s contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141831867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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