HX-groups are a natural generalization of groups that are similar in construction to hypergroups. However, they do not have to be considered as hypercompositional structures like hypergroups; instead, they are classical groups. After clarifying this difference between the two algebraic structures, we review the main properties of HX-groups, focusing on the regularity property. An HX-group G on a group G with the identity e is called regular whenever the identity E of G contains e. Any regular HX-group may be characterized as a group of cosets, and equivalent conditions for describing this property are established. New properties of HX-groups are discussed and illustrated by examples. These properties are uniformity and essentiality. In the second part of the paper, we introduce a new algebraic structure, that of HX-polygroups on a polygroup. Similarly to HX-groups, we propose some characterizations of HX-polygroups as polygroups of cosets or double cosets. We conclude the paper by proposing several lines of research related to HX-groups.
HX 群是群的自然概括，其构造与超群相似。然而，它们不必像超群那样被视为超组成结构；相反，它们是经典群。在澄清这两种代数结构的区别之后，我们将回顾 HX 群的主要性质，重点是正则性性质。只要 G 的标识 E 包含 e，那么在具有标识 e 的群 G 上的 HX 群 G 就称为正则群。任何正则 HX 群都可以表征为余集群，并建立了描述这一性质的等价条件。本文讨论了 HX 群的新性质，并通过实例加以说明。这些性质是均匀性和本质性。在论文的第二部分，我们引入了一种新的代数结构，即多群上的 HX 多群。与 HX 多群类似，我们提出了 HX 多群作为余集或双余集多群的一些特征。最后，我们提出了与 HX 多群相关的几个研究方向。
{"title":"From HX-Groups to HX-Polygroups","authors":"S. Mousavi, M. Jafarpour, Irina Cristea","doi":"10.3390/axioms13010007","DOIUrl":"https://doi.org/10.3390/axioms13010007","url":null,"abstract":"HX-groups are a natural generalization of groups that are similar in construction to hypergroups. However, they do not have to be considered as hypercompositional structures like hypergroups; instead, they are classical groups. After clarifying this difference between the two algebraic structures, we review the main properties of HX-groups, focusing on the regularity property. An HX-group G on a group G with the identity e is called regular whenever the identity E of G contains e. Any regular HX-group may be characterized as a group of cosets, and equivalent conditions for describing this property are established. New properties of HX-groups are discussed and illustrated by examples. These properties are uniformity and essentiality. In the second part of the paper, we introduce a new algebraic structure, that of HX-polygroups on a polygroup. Similarly to HX-groups, we propose some characterizations of HX-polygroups as polygroups of cosets or double cosets. We conclude the paper by proposing several lines of research related to HX-groups.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"11 2","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138953093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
With the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM), this paper introduces a variable selection method based on exponential square loss and the adaptive lasso penalty. Due to the non-convex and non-differentiable nature of this proposed method, convex programming is not applicable for its solution. We develop a block coordinate descent algorithm, decompose the exponential square component into the difference of two convex functions, and utilize the CCCP algorithm in combination with parabolic interpolation for optimizing problem-solving. Numerical simulations demonstrate that neglecting the spatial effects of error terms can lead to reduced accuracy in selecting zero coefficients in SEM. The proposed method demonstrates robustness even when noise is present in the observed values and when the spatial weights matrix is inaccurate. Finally, we apply the model to the Boston housing dataset.
随着空间数据在计量经济学和地理信息科学等领域的广泛应用，提高空间计量经济模型估计和变量选择鲁棒性的方法已成为研究的重点。本文以空间误差模型（SEM）为背景，介绍了一种基于指数平方损失和自适应套索惩罚的变量选择方法。由于该方法的非凸性和非可分性，凸编程并不适用于该方法的求解。我们开发了一种块坐标下降算法，将指数平方分量分解为两个凸函数之差，并利用 CCCP 算法与抛物线插值相结合来优化问题的解决。数值模拟证明，忽略误差项的空间效应会降低 SEM 中选择零系数的准确性。即使在观测值中存在噪声和空间权重矩阵不准确的情况下，所提出的方法也能表现出稳健性。最后，我们将该模型应用于波士顿住房数据集。
{"title":"Robust Variable Selection with Exponential Squared Loss for the Spatial Error Model","authors":"Shida Ma, Yiming Hou, Yunquan Song, Feng Zhou","doi":"10.3390/axioms13010004","DOIUrl":"https://doi.org/10.3390/axioms13010004","url":null,"abstract":"With the widespread application of spatial data in fields like econometrics and geographic information science, the methods to enhance the robustness of spatial econometric model estimation and variable selection have become a central focus of research. In the context of the spatial error model (SEM), this paper introduces a variable selection method based on exponential square loss and the adaptive lasso penalty. Due to the non-convex and non-differentiable nature of this proposed method, convex programming is not applicable for its solution. We develop a block coordinate descent algorithm, decompose the exponential square component into the difference of two convex functions, and utilize the CCCP algorithm in combination with parabolic interpolation for optimizing problem-solving. Numerical simulations demonstrate that neglecting the spatial effects of error terms can lead to reduced accuracy in selecting zero coefficients in SEM. The proposed method demonstrates robustness even when noise is present in the observed values and when the spatial weights matrix is inaccurate. Finally, we apply the model to the Boston housing dataset.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"38 6","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An essential aspect of healthcare is receiving an appropriate and opportune disease diagnosis. In recent years, there has been enormous progress in combining artificial intelligence to help professionals perform these tasks. The design of interval Type-3 fuzzy inference systems (IT3FIS) for medical classification is proposed in this work. This work proposed a genetic algorithm (GA) for the IT3FIS design where the fuzzy inputs correspond to attributes relational to a particular disease. This optimization allows us to find some main fuzzy inference systems (FIS) parameters, such as membership function (MF) parameters and the fuzzy if-then rules. As a comparison against the proposed method, the results achieved in this work are compared with Type-1 fuzzy inference systems (T1FIS), Interval Type-2 fuzzy inference systems (IT2FIS), and General Type-2 fuzzy inference systems (GT2FIS) using medical datasets such as Haberman’s Survival, Cryotherapy, Immunotherapy, PIMA Indian Diabetes, Indian Liver, and Breast Cancer Coimbra dataset, which achieved 75.30, 87.13, 82.04, 77.76, 71.86, and 71.06, respectively. Also, cross-validation tests were performed. Instances established as design sets are used to design the fuzzy inference systems, the optimization technique seeks to reduce the classification error using this set, and finally, the testing set allows the validation of the real performance of the FIS.
{"title":"Interval Type-3 Fuzzy Inference System Design for Medical Classification Using Genetic Algorithms","authors":"P. Melin, D. Sánchez, Oscar Castillo","doi":"10.3390/axioms13010005","DOIUrl":"https://doi.org/10.3390/axioms13010005","url":null,"abstract":"An essential aspect of healthcare is receiving an appropriate and opportune disease diagnosis. In recent years, there has been enormous progress in combining artificial intelligence to help professionals perform these tasks. The design of interval Type-3 fuzzy inference systems (IT3FIS) for medical classification is proposed in this work. This work proposed a genetic algorithm (GA) for the IT3FIS design where the fuzzy inputs correspond to attributes relational to a particular disease. This optimization allows us to find some main fuzzy inference systems (FIS) parameters, such as membership function (MF) parameters and the fuzzy if-then rules. As a comparison against the proposed method, the results achieved in this work are compared with Type-1 fuzzy inference systems (T1FIS), Interval Type-2 fuzzy inference systems (IT2FIS), and General Type-2 fuzzy inference systems (GT2FIS) using medical datasets such as Haberman’s Survival, Cryotherapy, Immunotherapy, PIMA Indian Diabetes, Indian Liver, and Breast Cancer Coimbra dataset, which achieved 75.30, 87.13, 82.04, 77.76, 71.86, and 71.06, respectively. Also, cross-validation tests were performed. Instances established as design sets are used to design the fuzzy inference systems, the optimization technique seeks to reduce the classification error using this set, and finally, the testing set allows the validation of the real performance of the FIS.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"119 13","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138958337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper discusses the multi-player non-cooperative game of nonlinear stochastic time-varying systems described by Itô-type differential equations in a finite time interval. Multi-player non-cooperative game problems are represented by multi-objective Pareto (MOP) control problems to describe the fact that each player has their own goals. By applying Hamilton–Jacobi inequalities (HJIs), the criterion of upper bounds of the MOP boundary is obtained for nonlinear stochastic systems, and the corresponding strategies are designed for such games, so the MOP problem is transformed into a HJI-constrained MOP problem. In order to overcome the difficulty of solving HJIs, a global linearization method is proposed to approximate the nonlinear systems. By the proposed global linearization method, multi-player non-cooperative game problems are transformed into Riccati equation-constrained MOP problems, and the approximate solutions of HJI-constrained MOP problems are obtained. Finally, a practical example is given to illustrate the effectiveness of the proposed method.
{"title":"Multi-Player Non-Cooperative Game Strategy of a Nonlinear Stochastic System with Time-Varying Parameters","authors":"Xiangyun Lin, Tongtong Zhang, Meilin Li, Rui Zhang, Weihai Zhang","doi":"10.3390/axioms13010003","DOIUrl":"https://doi.org/10.3390/axioms13010003","url":null,"abstract":"This paper discusses the multi-player non-cooperative game of nonlinear stochastic time-varying systems described by Itô-type differential equations in a finite time interval. Multi-player non-cooperative game problems are represented by multi-objective Pareto (MOP) control problems to describe the fact that each player has their own goals. By applying Hamilton–Jacobi inequalities (HJIs), the criterion of upper bounds of the MOP boundary is obtained for nonlinear stochastic systems, and the corresponding strategies are designed for such games, so the MOP problem is transformed into a HJI-constrained MOP problem. In order to overcome the difficulty of solving HJIs, a global linearization method is proposed to approximate the nonlinear systems. By the proposed global linearization method, multi-player non-cooperative game problems are transformed into Riccati equation-constrained MOP problems, and the approximate solutions of HJI-constrained MOP problems are obtained. Finally, a practical example is given to illustrate the effectiveness of the proposed method.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"86 13","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138957743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The standard pantograph delay equation (SPDDE) is one of the famous delay models. This standard model is basically homogeneous in nature and it has been extensively studied in the literature. However, the studies on the general inhomogeneous form of such a model seem rare. This paper considers the inhomogeneous pantograph delay equation (IPDDE) with a kind of arbitrary inhomogeneous term. This arbitrary inhomogeneous term is used in different forms to generate various classes of IPDDEs. The solutions of the present classes are obtained in closed series forms which satisfy the criteria of convergence. Also, the exact solutions are determined for these classes under a certain relation between the given initial condition of the model and the initial value of the inhomogeneous term. Several classes are generated and solved when the inhomogeneous term takes the form of trigonometric, exponential, and hyperbolic functions. Some existing results in the literature are recovered as special cases of the present ones. Moreover, the behaviors of the obtained solutions are demonstrated through graphs for various kinds of IPDDEs.
{"title":"Exact and Approximate Solutions for Some Classes of the Inhomogeneous Pantograph Equation","authors":"A. A. Al Qarni","doi":"10.3390/axioms13010001","DOIUrl":"https://doi.org/10.3390/axioms13010001","url":null,"abstract":"The standard pantograph delay equation (SPDDE) is one of the famous delay models. This standard model is basically homogeneous in nature and it has been extensively studied in the literature. However, the studies on the general inhomogeneous form of such a model seem rare. This paper considers the inhomogeneous pantograph delay equation (IPDDE) with a kind of arbitrary inhomogeneous term. This arbitrary inhomogeneous term is used in different forms to generate various classes of IPDDEs. The solutions of the present classes are obtained in closed series forms which satisfy the criteria of convergence. Also, the exact solutions are determined for these classes under a certain relation between the given initial condition of the model and the initial value of the inhomogeneous term. Several classes are generated and solved when the inhomogeneous term takes the form of trigonometric, exponential, and hyperbolic functions. Some existing results in the literature are recovered as special cases of the present ones. Moreover, the behaviors of the obtained solutions are demonstrated through graphs for various kinds of IPDDEs.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":" 3","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138960103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper performed an investigation into the s-embedding of the Lie superalgebra (→S1∣1), a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( SψD⊙) residing on the super-circle S1|1. We also introduce and rigorously define the central charge within the framework of (→S1∣1), leveraging the canonical central extension of SψD⊙. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra (→S1|1) is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.
{"title":"S-Embedding of Lie Superalgebras and Its Implications for Fuzzy Lie Algebras","authors":"Abdullah Assiry, Sabeur Mansour, A. Baklouti","doi":"10.3390/axioms13010002","DOIUrl":"https://doi.org/10.3390/axioms13010002","url":null,"abstract":"This paper performed an investigation into the s-embedding of the Lie superalgebra (→S1∣1), a representation of smooth vector fields on a (1,1)-dimensional super-circle. Our primary objective was to establish a precise definition of the s-embedding, effectively dissecting the Lie superalgebra into the superalgebra of super-pseudodifferential operators ( SψD⊙) residing on the super-circle S1|1. We also introduce and rigorously define the central charge within the framework of (→S1∣1), leveraging the canonical central extension of SψD⊙. Moreover, we expanded the scope of our inquiry to encompass the domain of fuzzy Lie algebras, seeking to elucidate potential connections and parallels between these ostensibly distinct mathematical constructs. Our exploration spanned various facets, including non-commutative structures, representation theory, central extensions, and central charges, as we aimed to bridge the gap between Lie superalgebras and fuzzy Lie algebras. To summarize, this paper is a pioneering work with two pivotal contributions. Initially, a meticulous definition of the s-embedding of the Lie superalgebra (→S1|1) is provided, emphasizing the representationof smooth vector fields on the (1,1)-dimensional super-circle, thereby enriching a fundamental comprehension of the topic. Moreover, an investigation of the realm of fuzzy Lie algebras was undertaken, probing associations with conventional Lie superalgebras. Capitalizing on these discoveries, we expound upon the nexus between central extensions and provide a novel deformed representation of the central charge.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":" 37","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138962080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact.
{"title":"Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain","authors":"Zhi-Jie Jiang","doi":"10.3390/axioms12121131","DOIUrl":"https://doi.org/10.3390/axioms12121131","url":null,"abstract":"Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"12 23","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138966159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jindong Liu, Huaigu Tian, Zhen Wang, Yan Guan, Zelin Cao
In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.
{"title":"Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System","authors":"Jindong Liu, Huaigu Tian, Zhen Wang, Yan Guan, Zelin Cao","doi":"10.3390/axioms12121125","DOIUrl":"https://doi.org/10.3390/axioms12121125","url":null,"abstract":"In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"1 6","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138996739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In mathematical analysis, the q-analogue of a function refers to a modified version of the function that is derived from q-series expansions. This paper is focused on the q-analogue of the exponential function and investigates a class of convex functions associated with it. The main objective is to derive precise inequalities that bound the coefficients of these convex functions. In this research, the initial coefficient bounds, Fekete–Szegő problem, second and third Hankel determinant have been determined. These coefficient bounds provide valuable information about the behavior and properties of the functions within the considered class.
{"title":"Coefficient Inequalities for q-Convex Functions with Respect to q-Analogue of the Exponential Function","authors":"Majid Khan, N. Khan, F. Tawfiq, Jong-Suk Ro","doi":"10.3390/axioms12121130","DOIUrl":"https://doi.org/10.3390/axioms12121130","url":null,"abstract":"In mathematical analysis, the q-analogue of a function refers to a modified version of the function that is derived from q-series expansions. This paper is focused on the q-analogue of the exponential function and investigates a class of convex functions associated with it. The main objective is to derive precise inequalities that bound the coefficients of these convex functions. In this research, the initial coefficient bounds, Fekete–Szegő problem, second and third Hankel determinant have been determined. These coefficient bounds provide valuable information about the behavior and properties of the functions within the considered class.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"24 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138998745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If λ denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to obtain a uniform approximation of a continuous vector-valued function by these operators when λ≥m+1. By using three-dimensional parametric plots, we illustrate this uniform approximation for some vector-valued functions. Finally, the influence in approximation by regular summability processes is studied, and their motivation is shown.
{"title":"Vector-Valued Shepard Processes: Approximation with Summability","authors":"O. Duman, B. Vecchia","doi":"10.3390/axioms12121124","DOIUrl":"https://doi.org/10.3390/axioms12121124","url":null,"abstract":"In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If λ denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to obtain a uniform approximation of a continuous vector-valued function by these operators when λ≥m+1. By using three-dimensional parametric plots, we illustrate this uniform approximation for some vector-valued functions. Finally, the influence in approximation by regular summability processes is studied, and their motivation is shown.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"54 4","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139000311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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