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Efficiency of a New Iterative Algorithm Using Fixed-Point Approach in the Settings of Uniformly Convex Banach Spaces 在均匀凸巴拿赫空间设置中使用定点法的新迭代算法的效率
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080502
R. Srivastava, Wakeel Ahmed, Asifa Tassaddiq, Nouf Alotaibi
{"title":"Efficiency of a New Iterative Algorithm Using Fixed-Point Approach in the Settings of Uniformly Convex Banach Spaces","authors":"R. Srivastava, Wakeel Ahmed, Asifa Tassaddiq, Nouf Alotaibi","doi":"10.3390/axioms13080502","DOIUrl":"https://doi.org/10.3390/axioms13080502","url":null,"abstract":"In the presence of Banach spaces, a novel iterative algorithm is presented in this study using the Chatterjea–Suzuki–C (CSC) condition, and the convergence theorems are established. The efficacy of the proposed algorithm is discussed analytically and numerically. We explain the solution of the Caputo fractional differential problem using our main result and then provide the numerical simulation to validate the results. Moreover, we use MATLAB R (2021a) to compare the obtained numerical results using the new iterative algorithm with some efficient existing algorithms. The work seems to contribute to the current advancement of fixed-point approximation iterative techniques in Banach spaces.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"116 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141802244","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 Unified Description of Abstract Convexity Structures 抽象凸面结构的统一描述
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080506
Chunrong Mo, Yanlong Yang
{"title":"The Unified Description of Abstract Convexity Structures","authors":"Chunrong Mo, Yanlong Yang","doi":"10.3390/axioms13080506","DOIUrl":"https://doi.org/10.3390/axioms13080506","url":null,"abstract":"The convexity of space is essential in nonlinear analysis, variational inequalities and optimization theory because it guarantees the existence and uniqueness of solutions to a certain extent. Because of its wide variety of applications, mathematicians have extensively promoted and researched convexity. This paper reviews some representative convexity structures and discusses their relations from their definitions, unifying them in the abstract convex structure. Moreover, applications of main convexity structures including KKM theory and fixed point theory will be reviewed.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"51 13","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799901","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 Impact of Quasi-Conformal Curvature Tensor on Warped Product Manifolds 准共形曲率张量对翘曲乘积流形的影响
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080500
Bang-Yen Chen, S. Shenawy, U.c. De, Alaa Rabie, Nasser Bin Turki
{"title":"The Impact of Quasi-Conformal Curvature Tensor on Warped Product Manifolds","authors":"Bang-Yen Chen, S. Shenawy, U.c. De, Alaa Rabie, Nasser Bin Turki","doi":"10.3390/axioms13080500","DOIUrl":"https://doi.org/10.3390/axioms13080500","url":null,"abstract":"This work investigates the effects on the factor manifolds of a singly warped product manifold resulting from the presence of a quasi-conformally flat, quasi-conformally symmetric, or divergence-free quasi-conformal curvature tensor. Quasi-conformally flat warped product manifolds exhibit three distinct scenarios: in one scenario, the base manifold has a constant curvature, while in the other two scenarios, it is quasi-Einstein. Alternatively, the fiber manifold has a constant curvature in two scenarios and is Einstein in one scenario. Quasi-conformally symmetric warped product manifolds present three distinct cases: in the first scenario, the base manifold is Ricci-symmetric and the fiber is Einstein; in the second case, the base manifold is Cartan-symmetric and the fiber has constant curvature; and in the last case, the fiber is Cartan-symmetric, and the Ricci tensor of the base manifold is of Codazzi type. Finally, conditions are provided for singly warped product manifolds that admit a divergence-free quasi-conformal curvature tensor to ensure that the Riemann curvature tensors of the factor manifolds are harmonic.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"23 9","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141800936","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
Numerical Solution of Third-Order Rosenau–Hyman and Fornberg–Whitham Equations via B-Spline Interpolation Approach 通过 B-样条插值法数值求解三阶罗森瑙-海曼和福恩贝格-维瑟姆方程
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080501
Tanveer Akbar, S. Haq, S. Arifeen, A. Iqbal
{"title":"Numerical Solution of Third-Order Rosenau–Hyman and Fornberg–Whitham Equations via B-Spline Interpolation Approach","authors":"Tanveer Akbar, S. Haq, S. Arifeen, A. Iqbal","doi":"10.3390/axioms13080501","DOIUrl":"https://doi.org/10.3390/axioms13080501","url":null,"abstract":"This study aims to find the numerical solution of the Rosenau–Hyman and Fornberg–Whitham equations via the quintic B-spline collocation method. Quintic B-spline, along with finite difference and theta-weighted schemes, is used for the discretization and approximation purposes. The effectiveness and robustness of the procedure is assessed by comparing the computed results with the exact and available results in the literature using absolute and relative error norms. The stability of the proposed scheme is studied using von Neumann stability analysis. Graphical representations are drawn to analyze the behavior of the solution.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"29 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801305","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
Geometry of Torsion Gerbes and Flat Twisted Vector Bundles 扭转矢量束和平面扭转矢量束的几何学
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080504
Byungdo Park
{"title":"Geometry of Torsion Gerbes and Flat Twisted Vector Bundles","authors":"Byungdo Park","doi":"10.3390/axioms13080504","DOIUrl":"https://doi.org/10.3390/axioms13080504","url":null,"abstract":"Gerbes and higher gerbes are geometric cocycles representing higher degree cohomology classes, and are attracting considerable interest in differential geometry and mathematical physics. We prove that a 2-gerbe has a torsion Dixmier–Douady class if and only if the gerbe has locally constant cocycle data. As an application, we give an alternative description of flat twisted vector bundles in terms of locally constant transition maps. These results generalize to n-gerbes for n=1 and n≥3, providing insights into the structure of higher gerbes and their applications to the geometry of twisted vector bundles.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"60 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141799308","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
Modelling Up-and-Down Moves of Binomial Option Pricing with Intuitionistic Fuzzy Numbers 用直觉模糊数模拟二项式期权定价的上下波动
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080503
J. D. Andrés-Sánchez
{"title":"Modelling Up-and-Down Moves of Binomial Option Pricing with Intuitionistic Fuzzy Numbers","authors":"J. D. Andrés-Sánchez","doi":"10.3390/axioms13080503","DOIUrl":"https://doi.org/10.3390/axioms13080503","url":null,"abstract":"Since the early 21st century, within fuzzy mathematics, there has been a stream of research in the field of option pricing that introduces vagueness in the parameters governing the movement of the underlying asset price through fuzzy numbers (FNs). This approach is commonly known as fuzzy random option pricing (FROP). In discrete time, most contributions use the binomial groundwork with up-and-down moves proposed by Cox, Ross, and Rubinstein (CRR), which introduces epistemic uncertainty associated with volatility through FNs. Thus, the present work falls within this stream of literature and contributes to the literature in three ways. First, analytical developments allow for the introduction of uncertainty with intuitionistic fuzzy numbers (IFNs), which are a generalization of FNs. Therefore, we can introduce bipolar uncertainty in parameter modelling. Second, a methodology is proposed that allows for adjusting the volatility with which the option is valued through an IFN. This approach is based on the existing developments in the literature on adjusting statistical parameters with possibility distributions via historical data. Third, we introduce into the debate on fuzzy random binomial option pricing the analytical framework that should be used in modelling upwards and downwards moves. In this sense, binomial modelling is usually employed to value path-dependent options that cannot be directly evaluated with the Black–Scholes–Merton (BSM) model. Thus, one way to assess the suitability of binomial moves for valuing a particular option is to approximate the results of the BSM in a European option with the same characteristics as the option of interest. In this study, we compared the moves proposed by Renddleman and Bartter (RB) with CRR. We have observed that, depending on the moneyness degree of the option and, without a doubt, on options traded at the money, RB modelling offers greater convergence to BSM prices than does CRR modelling.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"38 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141800124","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 Lebesgue Constants 关于勒贝格常数
Axioms Pub Date : 2024-07-26 DOI: 10.3390/axioms13080505
M. Ortigueira, G. Bengochea
{"title":"On Lebesgue Constants","authors":"M. Ortigueira, G. Bengochea","doi":"10.3390/axioms13080505","DOIUrl":"https://doi.org/10.3390/axioms13080505","url":null,"abstract":"Simple formulae for Lebesgue constants arising in the classical Fourier series approximation are obtained. Both even and odd cases are addressed, extending Fejér’s results. Asymptotic formulae are also obtained.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"3 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141801257","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
Existence Result for a Class of Time-Fractional Nonstationary Incompressible Navier–Stokes–Voigt Equations 一类时分数非稳态可压缩 Navier-Stokes-Voigt 方程的存在性结果
Axioms Pub Date : 2024-07-25 DOI: 10.3390/axioms13080499
Keji Xu, Biao Zeng
{"title":"Existence Result for a Class of Time-Fractional Nonstationary Incompressible Navier–Stokes–Voigt Equations","authors":"Keji Xu, Biao Zeng","doi":"10.3390/axioms13080499","DOIUrl":"https://doi.org/10.3390/axioms13080499","url":null,"abstract":"We are devoted in this work to dealing with a class of time-fractional nonstationary incompressible Navier–Stokes–Voigt equation involving the Caputo fractional derivative. By exploiting the properties of the operators in the equation, we use the Rothe method to show the existence of weak solutions to the equation by verifying all the conditions of the surjectivity theorem for nonlinear weakly continuous operators.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"15 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141804419","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 a Neumann Problem with an Intrinsic Operator 关于带有本征算子的诺伊曼问题
Axioms Pub Date : 2024-07-25 DOI: 10.3390/axioms13080497
D. Motreanu, A. Sciammetta
{"title":"On a Neumann Problem with an Intrinsic Operator","authors":"D. Motreanu, A. Sciammetta","doi":"10.3390/axioms13080497","DOIUrl":"https://doi.org/10.3390/axioms13080497","url":null,"abstract":"This paper investigates the existence and location of solutions for a Neumann problem driven by a (p,q) Laplacian operator and with a reaction term that depends not only on the solution and its gradient but also incorporates an intrinsic operator, which is its main novelty. This paper can be seen as the study of a quasilinear Neumann problem involving an elaborated perturbation with a Nemytskij operator. The approach proceeds through a version of the sub/supersolution method, exploiting an invariance property regarding the sub/supersolution ordered interval with respect to the intrinsic operator. An example illustrates the applicability of our result.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141804456","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 Fuzzy Logic for Semi-Overlap Functions and Their Residua 半重叠函数及其残差的模糊逻辑
Axioms Pub Date : 2024-07-25 DOI: 10.3390/axioms13080498
Lei Du, Songsong Dai, Lvqing Bi
{"title":"A Fuzzy Logic for Semi-Overlap Functions and Their Residua","authors":"Lei Du, Songsong Dai, Lvqing Bi","doi":"10.3390/axioms13080498","DOIUrl":"https://doi.org/10.3390/axioms13080498","url":null,"abstract":"Semi-overlap functions as a generalization of left-continuous t-norms also have residua. In this paper, we develop a new residuated logic, SOL-logic, based on semi-overlap functions and their residua. The corresponding algebraic structures, SOL-algebras, are defined, and the completeness of SOL with respect to SOL-algebras is proved.","PeriodicalId":502355,"journal":{"name":"Axioms","volume":"41 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141805840","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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