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Right Quantum Calculus on Finite Intervals with Respect to Another Function and Quantum Hermite–Hadamard Inequalities 有限区间上关于另一函数的右量子微积分和量子赫米特-哈达玛德不等式
Axioms Pub Date : 2024-07-10 DOI: 10.3390/axioms13070466
A. Cuntavepanit, Sotiris K. Ntouyas, J. Tariboon
{"title":"Right Quantum Calculus on Finite Intervals with Respect to Another Function and Quantum Hermite–Hadamard Inequalities","authors":"A. Cuntavepanit, Sotiris K. Ntouyas, J. Tariboon","doi":"10.3390/axioms13070466","DOIUrl":"https://doi.org/10.3390/axioms13070466","url":null,"abstract":"In this paper, we study right quantum calculus on finite intervals with respect to another function. We present new definitions on the right quantum derivative and right quantum integral of a function with respect to another function and study their basic properties. The new definitions generalize the previous existing results in the literature. We provide applications of the newly defined quantum calculus by obtaining new Hermite–Hadamard-type inequalities for convex, h-convex, and modified h-convex functions.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"36 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141660687","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
Fuzzy Milne, Ostrowski, and Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin Convexity and Their Applications 模糊米尔恩、奥斯特洛夫斯基和赫米特-哈达马德式不等式（Fuzzy Milne, Ostrowski, and Hermite-Hadamard-Type Inequalities for ħ-Godunova-Levin Convexity）及其应用
Axioms Pub Date : 2024-07-10 DOI: 10.3390/axioms13070465
Juan Wang, Valer-Daniel Breaz, Y. S. Hamed, Luminița-Ioana Cotîrlă, Xuewu Zuo
{"title":"Fuzzy Milne, Ostrowski, and Hermite–Hadamard-Type Inequalities for ħ-Godunova–Levin Convexity and Their Applications","authors":"Juan Wang, Valer-Daniel Breaz, Y. S. Hamed, Luminița-Ioana Cotîrlă, Xuewu Zuo","doi":"10.3390/axioms13070465","DOIUrl":"https://doi.org/10.3390/axioms13070465","url":null,"abstract":"In this paper, we establish several Milne-type inequalities for fuzzy number mappings and investigate their relationships with other inequalities. Specifically, we utilize Aumann’s integral and the fuzzy Kulisch–Miranker order, as well as the newly defined class, ħ-Godunova–Levin convex fuzzy number mappings, to derive Ostrowski’s and Hermite–Hadamard-type inequalities for fuzzy number mappings. Using the fuzzy Kulisch–Miranker order, we also establish connections with Hermite–Hadamard-type inequalities. Furthermore, we explore novel ideas and results based on Hermite–Hadamard–Fejér and provide examples and applications to illustrate our findings. Some very interesting examples are also provided to discuss the validation of the main results. Additionally, some new exceptional and classical outcomes have been obtained, which can be considered as applications of our main results.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"20 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141661715","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
Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains 无限域上的平滑逻辑实数和复数、普通和分数神经网络近似值
Axioms Pub Date : 2024-07-09 DOI: 10.3390/axioms13070462
G. Anastassiou
{"title":"Smooth Logistic Real and Complex, Ordinary and Fractional Neural Network Approximations over Infinite Domains","authors":"G. Anastassiou","doi":"10.3390/axioms13070462","DOIUrl":"https://doi.org/10.3390/axioms13070462","url":null,"abstract":"In this work, we study the univariate quantitative smooth approximations, including both real and complex and ordinary and fractional approximations, under different functions. The approximators presented here are neural network operators activated by Richard’s curve, a parametrized form of logistic sigmoid function. All domains used are obtained from the whole real line. The neural network operators used here are of the quasi-interpolation type: basic ones, Kantorovich-type ones, and those of the quadrature type. We provide pointwise and uniform approximations with rates. We finish with their applications.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"124 14","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141666418","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
Special Geometric Objects in Generalized Riemannian Spaces 广义黎曼空间中的特殊几何对象
Axioms Pub Date : 2024-07-09 DOI: 10.3390/axioms13070463
Marko Stefanović, Nenad O. Vesic, Dušan J. Simjanović, B. Randjelovic
{"title":"Special Geometric Objects in Generalized Riemannian Spaces","authors":"Marko Stefanović, Nenad O. Vesic, Dušan J. Simjanović, B. Randjelovic","doi":"10.3390/axioms13070463","DOIUrl":"https://doi.org/10.3390/axioms13070463","url":null,"abstract":"In this paper, we obtained the geometrical objects that are common in different definitions of the generalized Riemannian spaces. These objects are analogies to the Thomas projective parameter and the Weyl projective tensor. After that, we obtained some geometrical objects important for applications in physics.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"114 35","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141665675","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 Reduced-Dimension Weighted Explicit Finite Difference Method Based on the Proper Orthogonal Decomposition Technique for the Space-Fractional Diffusion Equation 基于适当正交分解技术的空间-分数扩散方程的降维加权显式有限差分法
Axioms Pub Date : 2024-07-08 DOI: 10.3390/axioms13070461
Xuehui Ren, Hong Li
{"title":"A Reduced-Dimension Weighted Explicit Finite Difference Method Based on the Proper Orthogonal Decomposition Technique for the Space-Fractional Diffusion Equation","authors":"Xuehui Ren, Hong Li","doi":"10.3390/axioms13070461","DOIUrl":"https://doi.org/10.3390/axioms13070461","url":null,"abstract":"A kind of reduced-dimension method based on a weighted explicit finite difference scheme and the proper orthogonal decomposition (POD) technique for diffusion equations with Riemann–Liouville fractional derivatives in space are discussed. The constructed approximation method written in matrix form can not only ensure a sufficient accuracy order but also reduce the degrees of freedom, decrease storage requirements, and accelerate the computation rate. Uniqueness, stabilization, and error estimation are demonstrated by matrix analysis. The procedural steps of the POD algorithm, which reduces dimensionality, are outlined. Numerical simulations to assess the viability and effectiveness of the reduced-dimension weighted explicit finite difference method are given. A comparison between the reduced-dimension method and the classical weighted explicit finite difference scheme is presented, including the error in the L2 norm, the accuracy order, and the CPU time.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"104 32","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141667405","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 Method for Calculating the Reliability of 2-Separable Networks and Its Applications 计算二可分离网络可靠性的方法及其应用
Axioms Pub Date : 2024-07-08 DOI: 10.3390/axioms13070459
Jing Liang, Haixing Zhao, Sun Xie
{"title":"A Method for Calculating the Reliability of 2-Separable Networks and Its Applications","authors":"Jing Liang, Haixing Zhao, Sun Xie","doi":"10.3390/axioms13070459","DOIUrl":"https://doi.org/10.3390/axioms13070459","url":null,"abstract":"This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"9 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141668225","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
The Split Equality Fixed-Point Problem and Its Applications 分割相等定点问题及其应用
Axioms Pub Date : 2024-07-08 DOI: 10.3390/axioms13070460
L. B. Mohammed, Adem Kilicman
{"title":"The Split Equality Fixed-Point Problem and Its Applications","authors":"L. B. Mohammed, Adem Kilicman","doi":"10.3390/axioms13070460","DOIUrl":"https://doi.org/10.3390/axioms13070460","url":null,"abstract":"It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life. To address this issue, we studied the SEFPP involving a class of quasi-pseudocontractive mappings in Hilbert spaces and constructed novel algorithms in this regard, and we proved the algorithms’ convergences both with and without prior knowledge of the operator norm for bounded and linear mappings. Additionally, we gave applications and numerical examples of our findings. A variety of well-known discoveries revealed in the literature are generalized by the findings presented in this work.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141667968","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
Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results 在数值方法新家族中实现最佳阶次：收敛和动态分析结果的启示
Axioms Pub Date : 2024-07-07 DOI: 10.3390/axioms13070458
Marlon Moscoso-Martínez, F. Chicharro, A. Cordero, J. Torregrosa, Gabriela Ureña-Callay
{"title":"Achieving Optimal Order in a Novel Family of Numerical Methods: Insights from Convergence and Dynamical Analysis Results","authors":"Marlon Moscoso-Martínez, F. Chicharro, A. Cordero, J. Torregrosa, Gabriela Ureña-Callay","doi":"10.3390/axioms13070458","DOIUrl":"https://doi.org/10.3390/axioms13070458","url":null,"abstract":"In this manuscript, we introduce a novel parametric family of multistep iterative methods designed to solve nonlinear equations. This family is derived from a damped Newton’s scheme but includes an additional Newton step with a weight function and a “frozen” derivative, that is, the same derivative than in the previous step. Initially, we develop a quad-parametric class with a first-order convergence rate. Subsequently, by restricting one of its parameters, we accelerate the convergence to achieve a third-order uni-parametric family. We thoroughly investigate the convergence properties of this final class of iterative methods, assess its stability through dynamical tools, and evaluate its performance on a set of test problems. We conclude that there exists one optimal fourth-order member of this class, in the sense of Kung–Traub’s conjecture. Our analysis includes stability surfaces and dynamical planes, revealing the intricate nature of this family. Notably, our exploration of stability surfaces enables the identification of specific family members suitable for scalar functions with a challenging convergence behavior, as they may exhibit periodical orbits and fixed points with attracting behavior in their corresponding dynamical planes. Furthermore, our dynamical study finds members of the family of iterative methods with exceptional stability. This property allows us to converge to the solution of practical problem-solving applications even from initial estimations very far from the solution. We confirm our findings with various numerical tests, demonstrating the efficiency and reliability of the presented family of iterative methods.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141670204","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
Visualization of Isometric Deformations of Helicoidal CMC Surfaces 螺旋曲面 CMC 的等距变形可视化
Axioms Pub Date : 2024-07-06 DOI: 10.3390/axioms13070457
Filip Vukojević, M. Antić
{"title":"Visualization of Isometric Deformations of Helicoidal CMC Surfaces","authors":"Filip Vukojević, M. Antić","doi":"10.3390/axioms13070457","DOIUrl":"https://doi.org/10.3390/axioms13070457","url":null,"abstract":"Helicoidal surfaces of constant mean curvature were fully described by do Carmo and Dajczer. However, the obtained parameterizations are given in terms of somewhat complicated integrals, and as a consequence, not many examples of such surfaces are visualized. In this paper, by using these methods in some particular cases, we provide several interesting visualizations involving these surfaces, mostly as an isometric deformation of a rotational surface. We also give interpretations of some older results involving helicoidal surfaces, motivated by the work carried out by Malkowsky and Veličković. All of the graphics in this paper were created in Wolfram Mathematica.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141671658","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
Concerning Transformations of Bases Associated with Unimodular diag(1, −1, −1)-Matrices 关于与单模斜（1，-1，-1）矩阵相关的基变换
Axioms Pub Date : 2024-07-04 DOI: 10.3390/axioms13070452
I. Shilin, Junesang Choi
{"title":"Concerning Transformations of Bases Associated with Unimodular diag(1, −1, −1)-Matrices","authors":"I. Shilin, Junesang Choi","doi":"10.3390/axioms13070452","DOIUrl":"https://doi.org/10.3390/axioms13070452","url":null,"abstract":"Considering a representation space for a group of unimodular diag(1, −1, −1)-matrices, we construct several bases whose elements are eigenfunctions of Casimir infinitesimal operators related to a reduction in the group to some one-parameter subgroups. Finding the kernels of base transformation integral operators in terms of special functions, we consider the compositions of some of these transformations. Since composition is a ‘closed’ operation on the set of base transformations, we obtain some integral relations for the special functions involved in the above kernels.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":" 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141678166","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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