Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-119
Indushree Mohan, Madhu Venkataraman
This paper presents and investigates three distinct kinds of analytic functions described by the Modified Tremblay Fractional Operator: IΥ[A,B], QΥ[A,B], and PΥ[A,B]. We give a detailed knowledge of these unique categories features by exploring majorization difficulties within them. By means of a careful analysis of majorization phenomena, we present a range of novel findings that demonstrate the significance of parameter specialisation in these classes. This work greatly expands our understanding of analytic functions and improves the field of mathematical analysis as a whole. To sum up, this study offers a comprehensive investigation of new analytic function classes, clarifies certain aspects of majorization, and makes significant contributions that broaden our understanding of complex analysis and geometric function theory.
{"title":"Majorization in Analytic Functions Among Distinct Classes Defined by Modified Tremblay Fractional Operator","authors":"Indushree Mohan, Madhu Venkataraman","doi":"10.28924/2291-8639-22-2024-119","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-119","url":null,"abstract":"This paper presents and investigates three distinct kinds of analytic functions described by the Modified Tremblay Fractional Operator: IΥ[A,B], QΥ[A,B], and PΥ[A,B]. We give a detailed knowledge of these unique categories features by exploring majorization difficulties within them. By means of a careful analysis of majorization phenomena, we present a range of novel findings that demonstrate the significance of parameter specialisation in these classes. This work greatly expands our understanding of analytic functions and improves the field of mathematical analysis as a whole. To sum up, this study offers a comprehensive investigation of new analytic function classes, clarifies certain aspects of majorization, and makes significant contributions that broaden our understanding of complex analysis and geometric function theory.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821037","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-113
N. Ravikumar, B. J. Chidananda, S. Latha
Herglotz representation and Bieberbach type properties are discussed for the q-analog classes of Janowski starlike and convex functions.
讨论了扬诺夫斯基星状函数和凸函数 q 类的赫格洛茨表示和比伯巴赫型性质。
{"title":"Subclasses of Janowski Associated with q-Derivative","authors":"N. Ravikumar, B. J. Chidananda, S. Latha","doi":"10.28924/2291-8639-22-2024-113","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-113","url":null,"abstract":"Herglotz representation and Bieberbach type properties are discussed for the q-analog classes of Janowski starlike and convex functions.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141822198","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-118
Waleed Al-Rawashdeh
In this study, we introduce and investigate a family of close-to-convex functions Sscc(λ,Ψ(x)) that associated with Horadam polynomials, functions in this family are defined with respect to symmetric conjugate points. The coefficient estimates of functions belonging to this family are derived. Moreover, we obtain the classical Fekete-Szegö inequality of functions belonging to this family.
{"title":"Applications of Horadam Polynomials to a Class of Close-to-Convex Functions","authors":"Waleed Al-Rawashdeh","doi":"10.28924/2291-8639-22-2024-118","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-118","url":null,"abstract":"In this study, we introduce and investigate a family of close-to-convex functions Sscc(λ,Ψ(x)) that associated with Horadam polynomials, functions in this family are defined with respect to symmetric conjugate points. The coefficient estimates of functions belonging to this family are derived. Moreover, we obtain the classical Fekete-Szegö inequality of functions belonging to this family.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821917","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-117
P. Indira, M. Jayalakshmi
Many problems appear to be arising in the present as a result of variations in transportation networks. The stochastic fixed-charge transportation problem (SFCTP) is one such problem. The SFCTP is transformed into a chance-constrained programming (CCP) problem where supply and demand are stochastic and objective functions are in a rough interval. In this model, to analyze the multi-objective rough interval stochastic fixed-charge transportation problem (MORISFCTP), where the objective function coefficients are represented by rough intervals and the supply and destination factors are probabilistic constraints. This model operates an expected value operator to deal with uncertainty, in which the coefficient of the objective functions in the fuzzy is changed to a crisp form, and the probabilistic constraints are converted to a deterministic form by the Weibull distribution. To produce the optimal compromise solutions of the proposed model, three distinct methods are used: the fuzzy programming approach, the method of a linear weighted sum, and the €-constraint method. Lastly, the paper delivers a practical illustration of a MORISFCTP to demonstrate the usefulness and feasibility of the suggested methodology.
{"title":"Prediction of Stochastic Transportation Problem with Fixed Charge in Multi-Objective Rough Interval Environment","authors":"P. Indira, M. Jayalakshmi","doi":"10.28924/2291-8639-22-2024-117","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-117","url":null,"abstract":"Many problems appear to be arising in the present as a result of variations in transportation networks. The stochastic fixed-charge transportation problem (SFCTP) is one such problem. The SFCTP is transformed into a chance-constrained programming (CCP) problem where supply and demand are stochastic and objective functions are in a rough interval. In this model, to analyze the multi-objective rough interval stochastic fixed-charge transportation problem (MORISFCTP), where the objective function coefficients are represented by rough intervals and the supply and destination factors are probabilistic constraints. This model operates an expected value operator to deal with uncertainty, in which the coefficient of the objective functions in the fuzzy is changed to a crisp form, and the probabilistic constraints are converted to a deterministic form by the Weibull distribution. To produce the optimal compromise solutions of the proposed model, three distinct methods are used: the fuzzy programming approach, the method of a linear weighted sum, and the €-constraint method. Lastly, the paper delivers a practical illustration of a MORISFCTP to demonstrate the usefulness and feasibility of the suggested methodology.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823788","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-115
M.H.M. Rashid, S. Al-Subh
In this paper, we have introduced the concept of the set of rough I3-lacunary limit points for triple sequences in 2-normed spaces. We have established statistical convergence requirements associated with this set. Furthermore, we have introduced the idea of rough I3-lacunary statistical convergence for triple sequences. Additionally, we have demonstrated that this set of rough I3-lacunary limit points is both convex and closed within the context of a 2-normed space. We have also explored the relationships between a sequence’s rough I3-lacunary statistical cluster points and its rough I3-lacunary statistical limit points in the same 2-normed space. Expanding upon the concept of triple sequence spaces, we have introduced the notion of Wijsman I3-Cesáro summability for triple sequences. In doing so, we have investigated the connections between Wijsman strongly I3-Cesáro summability and Wijsman statistical I3-Cesáro summability. Furthermore, we have introduced the concepts of Wijsman rough strongly p-lacunary summability of order α and Wijsman rough lacunary statistical convergence of order α for triple sequences. These new concepts have been subjected to a thorough examination to understand their characteristics, and we have explored potential connections between them. Additionally, we have investigated how these newly introduced concepts relate to existing notions in the literature.
{"title":"Statistical Convergence with Rough I3-Lacunary and Wijsman Rough I3-Statistical Convergence in 2-Normed Spaces","authors":"M.H.M. Rashid, S. Al-Subh","doi":"10.28924/2291-8639-22-2024-115","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-115","url":null,"abstract":"In this paper, we have introduced the concept of the set of rough I3-lacunary limit points for triple sequences in 2-normed spaces. We have established statistical convergence requirements associated with this set. Furthermore, we have introduced the idea of rough I3-lacunary statistical convergence for triple sequences. Additionally, we have demonstrated that this set of rough I3-lacunary limit points is both convex and closed within the context of a 2-normed space. We have also explored the relationships between a sequence’s rough I3-lacunary statistical cluster points and its rough I3-lacunary statistical limit points in the same 2-normed space. Expanding upon the concept of triple sequence spaces, we have introduced the notion of Wijsman I3-Cesáro summability for triple sequences. In doing so, we have investigated the connections between Wijsman strongly I3-Cesáro summability and Wijsman statistical I3-Cesáro summability. Furthermore, we have introduced the concepts of Wijsman rough strongly p-lacunary summability of order α and Wijsman rough lacunary statistical convergence of order α for triple sequences. These new concepts have been subjected to a thorough examination to understand their characteristics, and we have explored potential connections between them. Additionally, we have investigated how these newly introduced concepts relate to existing notions in the literature.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823690","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-114
Muhammad Aslam, Osama H. Arif
In this paper, we introduce a regression model using dummy variables within the framework of neutrosophic statistics. This model is designed for regression analysis under conditions of uncertainty, extending the classical regression model with dummy variables. We also present regression and analysis of variance under neutrosophic statistics. The application of our model is demonstrated through simulation and comparative studies, showing that the results differ from those obtained using classical regression. Our findings indicate that the degree of uncertainty significantly impacts the predicted and residual values.
{"title":"Neutrosophic Regression Modeling with Dummy Variables: Applications and Simulations","authors":"Muhammad Aslam, Osama H. Arif","doi":"10.28924/2291-8639-22-2024-114","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-114","url":null,"abstract":"In this paper, we introduce a regression model using dummy variables within the framework of neutrosophic statistics. This model is designed for regression analysis under conditions of uncertainty, extending the classical regression model with dummy variables. We also present regression and analysis of variance under neutrosophic statistics. The application of our model is demonstrated through simulation and comparative studies, showing that the results differ from those obtained using classical regression. Our findings indicate that the degree of uncertainty significantly impacts the predicted and residual values.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141820526","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-116
M. Kankarej
In the present paper I have explored the properties of complete and horizontal lifts of an almost product structure. Its partial integrability and integrability conditions on the tangent bundle are part of this study. Along with different theorems on the lifts the prolongation of an almost product structure on the third tangent bundle T3M has been explored.
{"title":"Lifts of Almost Product Structures From Manifolds to Tangent Bundles","authors":"M. Kankarej","doi":"10.28924/2291-8639-22-2024-116","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-116","url":null,"abstract":"In the present paper I have explored the properties of complete and horizontal lifts of an almost product structure. Its partial integrability and integrability conditions on the tangent bundle are part of this study. Along with different theorems on the lifts the prolongation of an almost product structure on the third tangent bundle T3M has been explored.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141820918","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}
Pub Date : 2024-07-19DOI: 10.28924/2291-8639-22-2024-120
R. A. Rashwan, H. Hammad, Mohamed Gamal, Saleh Omran, M. De La Sen
The explicit aim of this manuscript is to obtain fixed point consequences under novel ψ-contraction mappings in a complete cone metric space over Banach algebra. We connect and relate different fixed point theorems by using the idea of ψ-contraction mappings, providing a thorough viewpoint that deepens our comprehension of this topic. Our theorems generalize and unify many results in the scientific literature. These prospective extensions offer intriguing research directions and have the potential to further advance the study of fixed point theory. The investigation of examples plays an extremely crucial role in verifying the effectiveness and validity of our theoretical results. Moreover, to support the theoretical results, some examples are investigated to emphasize these results. Ultimately, the existence and uniqueness of the solution to the Urysohn integral and nonlinear fractional differential equation are cooperated as applications to provide an authoritative basis for dealing with actual problems that include these equations.
{"title":"Fixed Point Methodologies for ψ-Contraction Mappings in Cone Metric Spaces over Banach Algebra with Supportive Applications","authors":"R. A. Rashwan, H. Hammad, Mohamed Gamal, Saleh Omran, M. De La Sen","doi":"10.28924/2291-8639-22-2024-120","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-120","url":null,"abstract":"The explicit aim of this manuscript is to obtain fixed point consequences under novel ψ-contraction mappings in a complete cone metric space over Banach algebra. We connect and relate different fixed point theorems by using the idea of ψ-contraction mappings, providing a thorough viewpoint that deepens our comprehension of this topic. Our theorems generalize and unify many results in the scientific literature. These prospective extensions offer intriguing research directions and have the potential to further advance the study of fixed point theory. The investigation of examples plays an extremely crucial role in verifying the effectiveness and validity of our theoretical results. Moreover, to support the theoretical results, some examples are investigated to emphasize these results. Ultimately, the existence and uniqueness of the solution to the Urysohn integral and nonlinear fractional differential equation are cooperated as applications to provide an authoritative basis for dealing with actual problems that include these equations.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141823932","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}
Pub Date : 2024-07-09DOI: 10.28924/2291-8639-22-2024-110
A. Uma, R. Swaminathan
A mathematical model of carbon dioxide (CO2) absorption in an aqueous solution consisting of two reactants, 2-amino-2-methyl-1-proponal and 1,8-diamino-p-methane is considered. Akbari Ganji Method and Differential Transform Method are implemented to resolve the system of nonlinear equations, yielding an analytical formulation for the concentration of carbon dioxide, 2-amino-2-methyl-1-proponal, 1,8-diamino-p-methane and the molar flux in-terms of reaction rate constants. The obtained analytical findings are used to evaluate the different diffusion parameters and compared with numerical results. By assessing Matlab results with analytical findings, a successful outcome is discovered. Moreover, the influence of parameters on molar flux is examined. Also, graphical representations are presented and discussed here. The new analytical results contribute to optimizing the consistency of this model. The ensuring outcomes have been verified utilizing the existing numerical data with prior findings, and we are then presented with an adequate level of agreement.
{"title":"Mathematical Analysis of Nonlinear Reaction Diffusion Process at Carbon Dioxide Absorption in Concentrated Mixtures of 2-Amino-2-Methyl-1-Proponal and 1,8-Diamino-p-Methane","authors":"A. Uma, R. Swaminathan","doi":"10.28924/2291-8639-22-2024-110","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-110","url":null,"abstract":"A mathematical model of carbon dioxide (CO2) absorption in an aqueous solution consisting of two reactants, 2-amino-2-methyl-1-proponal and 1,8-diamino-p-methane is considered. Akbari Ganji Method and Differential Transform Method are implemented to resolve the system of nonlinear equations, yielding an analytical formulation for the concentration of carbon dioxide, 2-amino-2-methyl-1-proponal, 1,8-diamino-p-methane and the molar flux in-terms of reaction rate constants. The obtained analytical findings are used to evaluate the different diffusion parameters and compared with numerical results. By assessing Matlab results with analytical findings, a successful outcome is discovered. Moreover, the influence of parameters on molar flux is examined. Also, graphical representations are presented and discussed here. The new analytical results contribute to optimizing the consistency of this model. The ensuring outcomes have been verified utilizing the existing numerical data with prior findings, and we are then presented with an adequate level of agreement.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664358","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}
Pub Date : 2024-07-09DOI: 10.28924/2291-8639-22-2024-112
M. Palanikumar, G. Mohanraj, A. Iampan
We introduce three sequences of different prime bi-ideals of semirings such that 11(12,13)-prime bi-ideal, 21(22)-prime bi-ideal and 31(32,33)-prime bi-ideal using bi-ideals. In this article, we characterize the different prime bi-ideals. We discuss that the 11-prime bi-ideal implies the 12-prime bi-ideal implies the 13-prime bi-ideal, but the reverse implication does not hold with the help of numerical examples. We investigate if a 21-prime bi-ideal implies a 22-prime bi-ideal, but the converse need not be true with the help of numerical examples. If G is any bi-ideal of a semiring S, then K(G) = {x ∈ G | x + y = z for some y, z ∈ G} is the unique largest k-bi-ideal contained in G. If Θ is a 21-prime bi-ideal of S, then Θ is a one-sided ideal of S. It is shown that there is a relation between G and K(G), in which G is a 13-prime bi-ideal. In our communication, 11-prime bi-ideal implies 21-prime bi-ideal. An interaction between a 31-prime bi-ideal implies a 32-prime bi-ideal, and a 32-prime bi-ideal implies a 33-prime bi-ideal; however, the reverse implication is invalid by some examples. Every 13-prime bi-ideal is a 22-prime bi-ideal, but the converse need not be true with the help of examples.
我们用双ideals引入了三个序列的不同质半ideals，如11(12,13)-质半ideals、21(22)-质半ideals和31(32,33)-质半ideals。在本文中，我们描述了不同质数双理想的特征。我们讨论了 11-prime 双理想意味着 12-prime 双理想意味着 13-prime 双理想，但在数字实例的帮助下，反向蕴涵并不成立。我们研究 21 原数双偶数是否蕴含 22 原数双偶数，但反向蕴含不一定成立，这需要借助数字实例。如果 G 是半配系 S 的任意一个双ideal，那么 K(G) = {x∈G | x + y = z for some y, z∈G} 是包含在 G 中的唯一最大的 k-bi-ideal 。在我们的交流中，11-质双理想意味着 21-质双理想。31-prime 双理想之间的相互作用意味着 32-prime 双理想，32-prime 双理想意味着 33-prime 双理想；然而，从某些例子来看，反向蕴涵是无效的。每一个 13 素二理想都是一个 22 素二理想，但举例说明，反向蕴涵不一定成立。
{"title":"Characterization of Different Prime Bi-Ideals and Its Generalization of Semirings","authors":"M. Palanikumar, G. Mohanraj, A. Iampan","doi":"10.28924/2291-8639-22-2024-112","DOIUrl":"https://doi.org/10.28924/2291-8639-22-2024-112","url":null,"abstract":"We introduce three sequences of different prime bi-ideals of semirings such that 11(12,13)-prime bi-ideal, 21(22)-prime bi-ideal and 31(32,33)-prime bi-ideal using bi-ideals. In this article, we characterize the different prime bi-ideals. We discuss that the 11-prime bi-ideal implies the 12-prime bi-ideal implies the 13-prime bi-ideal, but the reverse implication does not hold with the help of numerical examples. We investigate if a 21-prime bi-ideal implies a 22-prime bi-ideal, but the converse need not be true with the help of numerical examples. If G is any bi-ideal of a semiring S, then K(G) = {x ∈ G | x + y = z for some y, z ∈ G} is the unique largest k-bi-ideal contained in G. If Θ is a 21-prime bi-ideal of S, then Θ is a one-sided ideal of S. It is shown that there is a relation between G and K(G), in which G is a 13-prime bi-ideal. In our communication, 11-prime bi-ideal implies 21-prime bi-ideal. An interaction between a 31-prime bi-ideal implies a 32-prime bi-ideal, and a 32-prime bi-ideal implies a 33-prime bi-ideal; however, the reverse implication is invalid by some examples. Every 13-prime bi-ideal is a 22-prime bi-ideal, but the converse need not be true with the help of examples.","PeriodicalId":45204,"journal":{"name":"International Journal of Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141664795","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}
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