Pub Date : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4946
Javier A. Hassan, Aziz B. Tapeing, Hounam B. Copel, Alcyn R. Bakkang, Sharifa Dianne A. Aming
Let G be a graph. A subset I′ of a vertex-set V (G) of G is called a J2-independent in Gif for every pair of distinct vertices a, b ∈ I′, dG(a, b) ̸= 1, N2 G[a]N2 G[b] ̸= ∅ and N2 G[b]N2 G[a] ̸= ∅. The maximum cardinality among all J2-independent sets in G, denoted by αJ2 (G), is called the J2-independence number of G. Any J2-independent set I′satisfying |I′| = αJ2 (G) is called the maximum J2-independent set of G or an αJ2 -set of G. In this paper, we establish some boundsof this parameter on a generalized graph, join and corona of two graphs. We characterize J2-independent sets in some families of graphs, and we use these results to derive the exact values of parameters of these graphs. Moreover, we investigate the connections of this new parameter with other variants of independence parameters. In fact, we show that the J2-independence number of a graph is always less than or equal to the standard independence number.
设 G 是一个图。如果每一对不同的顶点 a、b ∈ I′，dG(a, b) ̸= 1，N2 G[a]N2 G[b] ̸= ∅，且 N2 G[b]N2 G[a] ̸= ∅，则 G 的顶点集 V（G）的子集 I′称为 G 中的 J2 独立集。满足 |I′| = αJ2 (G) 的任何 J2 独立集 I′ 都称为 G 的最大 J2 独立集或 G 的 αJ2 集。我们描述了一些图形族中与 J2 无关的集合的特征，并利用这些结果推导出这些图形参数的精确值。此外，我们还研究了这一新参数与其他独立参数变体之间的联系。事实上，我们证明了图形的 J2-独立性数总是小于或等于标准独立性数。
{"title":"$J^2$-Independence Parameters of Some Graphs","authors":"Javier A. Hassan, Aziz B. Tapeing, Hounam B. Copel, Alcyn R. Bakkang, Sharifa Dianne A. Aming","doi":"10.29020/nybg.ejpam.v17i1.4946","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4946","url":null,"abstract":"Let G be a graph. A subset I′ of a vertex-set V (G) of G is called a J2-independent in Gif for every pair of distinct vertices a, b ∈ I′, dG(a, b) ̸= 1, N2 G[a]N2 G[b] ̸= ∅ and N2 G[b]N2 G[a] ̸= ∅. The maximum cardinality among all J2-independent sets in G, denoted by αJ2 (G), is called the J2-independence number of G. Any J2-independent set I′satisfying |I′| = αJ2 (G) is called the maximum J2-independent set of G or an αJ2 -set of G. In this paper, we establish some boundsof this parameter on a generalized graph, join and corona of two graphs. We characterize J2-independent sets in some families of graphs, and we use these results to derive the exact values of parameters of these graphs. Moreover, we investigate the connections of this new parameter with other variants of independence parameters. In fact, we show that the J2-independence number of a graph is always less than or equal to the standard independence number.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140471534","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4992
Mohamed Ahmed Sidaty
We study some properties of the spaces λ(E) of weakly λ-summable sequences and λ⟨E⟩ of strongly λ-summable sequences of a locally convex space E. For example, after proving results on bounded sets of these spaces, we express the elements of their K öthe duals in terms of sequences in the continuous dual E′ of E, then we prove that these spaces possess the AK property if and only if the K ̈othe dual coincides with the continuous dual.
我们研究局部凸空间 E 的弱λ可求和序列空间 λ(E) 和强λ可求和序列空间 λ⟨E⟩ 的一些性质。例如，在证明了这些空间的有界集的结果之后，我们用 E 的连续对偶 E′中的序列来表达它们的 K öthe 对偶的元素，然后我们证明，当且仅当 K ̈othe 对偶与连续对偶重合时，这些空间才具有 AK 性质。
{"title":"Köthe Dual of Some Vector-valued Sequence Spaces","authors":"Mohamed Ahmed Sidaty","doi":"10.29020/nybg.ejpam.v17i1.4992","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4992","url":null,"abstract":"We study some properties of the spaces λ(E) of weakly λ-summable sequences and λ⟨E⟩ of strongly λ-summable sequences of a locally convex space E. For example, after proving results on bounded sets of these spaces, we express the elements of their K öthe duals in terms of sequences in the continuous dual E′ of E, then we prove that these spaces possess the AK property if and only if the K ̈othe dual coincides with the continuous dual.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140476256","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5025
Kholood Alnefaie
In the present paper, we apply the concept of reverse derivation in rings on the concept of d − algebra to obtain the concept called a left-right (resp. right-left) reverse derivations of d−algebra X (briefly, (l, r) resp. (r, l)− reverse derivation of d − algebra ), we will also, define some concepts such as regular map, composition two maps and study the related properties. Moreover, the notions of partial ordered edge d − algebra as well as d − subalgebra and their relation to our current study are obtained. In addition, some illustrative examples and counterexamples are discussed.
在本文中，我们将环中反向推导的概念应用于 d - 代数的概念上，从而得到了称为 d - 代数 X 的左-右（或右-左）反向推导的概念（简言之，d - 代数的（l, r）或（r, l）-反向推导），我们还将定义一些概念，如正则映射、两个映射的组成，并研究其相关性质。此外，我们还将获得部分有序边 d - 代数和 d - 子代数的概念，以及它们与我们当前研究的关系。此外，还讨论了一些示例和反例。
{"title":"On Reverse Derivations in d-algebras","authors":"Kholood Alnefaie","doi":"10.29020/nybg.ejpam.v17i1.5025","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5025","url":null,"abstract":"\u0000\u0000\u0000In the present paper, we apply the concept of reverse derivation in rings on the concept of d − algebra to obtain the concept called a left-right (resp. right-left) reverse derivations of d−algebra X (briefly, (l, r) resp. (r, l)− reverse derivation of d − algebra ), we will also, define some concepts such as regular map, composition two maps and study the related properties. Moreover, the notions of partial ordered edge d − algebra as well as d − subalgebra and their relation to our current study are obtained. In addition, some illustrative examples and counterexamples are discussed.\u0000\u0000\u0000","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140473516","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5027
Ahlam Ahmed Alharbi, Adem Kilicman
The main objective of this research is to study some types of generalized closed sets in fuzzy bitopology including $(i,j)-galpha-cld$, $(i,j)-gs-cld$, $(i,j)-gp-cld$, and $(i,j)-gbeta-cld$. We then present basic theorems for determining their relationships and explain their properties, such as closure and interior. In addition, there are many interesting counterexamples. The last part of the research focuses on generalized compactness in fuzzy bitopological spaces and their types and explores the relationships between these concepts, their important theories, and some relevant counterexamples. The results established in this paper are new in the domain of fuzzy bitopology.
{"title":"On Generalized Compactness in Fuzzy Bitopological Spaces","authors":"Ahlam Ahmed Alharbi, Adem Kilicman","doi":"10.29020/nybg.ejpam.v17i1.5027","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5027","url":null,"abstract":"The main objective of this research is to study some types of generalized closed sets in fuzzy bitopology including $(i,j)-galpha-cld$, $(i,j)-gs-cld$, $(i,j)-gp-cld$, and $(i,j)-gbeta-cld$. We then present basic theorems for determining their relationships and explain their properties, such as closure and interior. In addition, there are many interesting counterexamples. The last part of the research focuses on generalized compactness in fuzzy bitopological spaces and their types and explores the relationships between these concepts, their important theories, and some relevant counterexamples. The results established in this paper are new in the domain of fuzzy bitopology.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140475164","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5050
M. Al-Mazmumy, Mona Alsulami
The Bagley-Torvik equation is an imperative differential equation that considerably arises in various branches of mathematical physics and mechanics. However, very few methods exist for the treatment of the model analytically; in fact, researchers frequently shop for semi-analytical and numerical methods in their studies. Therefore, the main goal of this research is to find theexact analytical solution for the fractional Bagley-Torvik equation fitted with Dirichlet boundary data, as well as a system of fractional Bagley-Torvik equations. Thus, this research aims to show that the modified Adomian decomposition method (MADM) via the proposed two algorithms is a very effective method for treating a class of Bagley-Torvik equations endowed with Dirichletboundary data. Certainly, MADM is a very powerful approach for solving dissimilar functional equations without the need for either linearization, discretization, perturbation, or even unnecessary restraining postulations. Additionally, the method reveals exact analytical solutions whenever obtainable or closed-form series solutions whenever exact solutions are not feasible. Lastly, some illustrative test problems of the governing model are examined to demonstrate the superiority of the proposed algorithms.
{"title":"Utilization of the Modified Adomian Decomposition Method on the Bagley-Torvik Equation Amidst Dirichlet Boundary Conditions","authors":"M. Al-Mazmumy, Mona Alsulami","doi":"10.29020/nybg.ejpam.v17i1.5050","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5050","url":null,"abstract":"The Bagley-Torvik equation is an imperative differential equation that considerably arises in various branches of mathematical physics and mechanics. However, very few methods exist for the treatment of the model analytically; in fact, researchers frequently shop for semi-analytical and numerical methods in their studies. Therefore, the main goal of this research is to find theexact analytical solution for the fractional Bagley-Torvik equation fitted with Dirichlet boundary data, as well as a system of fractional Bagley-Torvik equations. Thus, this research aims to show that the modified Adomian decomposition method (MADM) via the proposed two algorithms is a very effective method for treating a class of Bagley-Torvik equations endowed with Dirichletboundary data. Certainly, MADM is a very powerful approach for solving dissimilar functional equations without the need for either linearization, discretization, perturbation, or even unnecessary restraining postulations. Additionally, the method reveals exact analytical solutions whenever obtainable or closed-form series solutions whenever exact solutions are not feasible. Lastly, some illustrative test problems of the governing model are examined to demonstrate the superiority of the proposed algorithms.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140474582","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5005
Rania Saadeh, Al-anoud Alshawabkeh, Raed Khalil, Mohamed A. Abdoon, Nidal E. Taha, Dalal Khalid Almutairi
In recent years, Mohanad transform, a mathematical approach, has drawn a lot of interest from researchers. It is useful for solving many engineering and scientific problems, such as those involving electric circuits, population growth, vibrational beams, and heat conduction. The Mohanad transform is defined and introduced in this study, along with its fundamental qualities,including linearity and convolution. It is also discussed in connection with other integral transforms and how it is used in derivatives. Additionally, we use the Mohanad transform to solve a few systems of ordinary differential equations (ODEs) and review its properties in this paper. Determining the concentration of a chemical reactant (material) in a series is a physical chemistry problem that we use in the application part. We achieve this by developing a model based on ordinary differential equations (ODEs) and then solving them using the Mohanad transform. This research proves that, with little computational effort, we can get the exact solutions of ordinary differential equations (ODEs) via the Mohanad transform. We used graphs and tables to show our answer.
{"title":"The Mohanad Transforms and Their Applications for Solving Systems of Differential Equations","authors":"Rania Saadeh, Al-anoud Alshawabkeh, Raed Khalil, Mohamed A. Abdoon, Nidal E. Taha, Dalal Khalid Almutairi","doi":"10.29020/nybg.ejpam.v17i1.5005","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5005","url":null,"abstract":"In recent years, Mohanad transform, a mathematical approach, has drawn a lot of interest from researchers. It is useful for solving many engineering and scientific problems, such as those involving electric circuits, population growth, vibrational beams, and heat conduction. The Mohanad transform is defined and introduced in this study, along with its fundamental qualities,including linearity and convolution. It is also discussed in connection with other integral transforms and how it is used in derivatives. Additionally, we use the Mohanad transform to solve a few systems of ordinary differential equations (ODEs) and review its properties in this paper. Determining the concentration of a chemical reactant (material) in a series is a physical chemistry problem that we use in the application part. We achieve this by developing a model based on ordinary differential equations (ODEs) and then solving them using the Mohanad transform. This research proves that, with little computational effort, we can get the exact solutions of ordinary differential equations (ODEs) via the Mohanad transform. We used graphs and tables to show our answer.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140474750","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5009
Feng Zhang, Chunwen Zhang
In this paper, we prove that all the eigenvalues of arbitrarily complex matrix are located in one closed disk, which is a refinement of some existing inequalities.
在本文中，我们证明了任意复杂矩阵的所有特征值都位于一个封闭的圆盘中，这是对现有一些不等式的完善。
{"title":"Matrix Mixed Inequalities","authors":"Feng Zhang, Chunwen Zhang","doi":"10.29020/nybg.ejpam.v17i1.5009","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5009","url":null,"abstract":"In this paper, we prove that all the eigenvalues of arbitrarily complex matrix are located in one closed disk, which is a refinement of some existing inequalities.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140479927","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5004
Waleed AlRawashdeh
In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $mathcal{F}(n, alpha, beta)$, that depends on the Ruscheweyh operator. For functions in this class, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg"{o} inequality of functions belonging to this class.
{"title":"Fekete-Szegö Functional of a Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials","authors":"Waleed AlRawashdeh","doi":"10.29020/nybg.ejpam.v17i1.5004","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5004","url":null,"abstract":"In this paper, we introduce and investigate a class of bi-univalent functions, denoted by $mathcal{F}(n, alpha, beta)$, that depends on the Ruscheweyh operator. For functions in this class, we derive the estimations for the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$. Moreover, we obtain the classical Fekete-Szeg\"{o} inequality of functions belonging to this class.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140474182","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.5011
Dae San Kim, Taekyun Kim, J. Kwon
In this paper, we consider various Stirling numbers of both kinds, including the unsigned degenerate Stirling numbers of the first kind, the degenerate Stirling numbers of the second kind, the unsigned degenerate r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind. The aim of this paper is by using generating functions to further study explicit expressions, some identities and equivalent relations for those Stirling numbers.
{"title":"Study on Degenerate Stirling Numbers","authors":"Dae San Kim, Taekyun Kim, J. Kwon","doi":"10.29020/nybg.ejpam.v17i1.5011","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.5011","url":null,"abstract":"In this paper, we consider various Stirling numbers of both kinds, including the unsigned degenerate Stirling numbers of the first kind, the degenerate Stirling numbers of the second kind, the unsigned degenerate r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind. The aim of this paper is by using generating functions to further study explicit expressions, some identities and equivalent relations for those Stirling numbers.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140475268","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 : 2024-01-31DOI: 10.29020/nybg.ejpam.v17i1.4952
M. Alshayea, K. Alsager
The main objective of this paper is to effectively define a new concept of the fabulous fuzzy set theory that is called m-polar Q-hesitant anti-fuzzy set and apply it to the BCK/BCI-algebras. The m-polar Q-hesitant anti-fuzzy set is an astonishing development of the combination between the m-polar fuzzy set and the Q-hesitant fuzzy set. However, we introduce knowledge of the m-polar Q-hesitant anti-fuzzy subalgebra, m-polar Q-hesitant anti-fuzzy ideal, closed m-polar Q-hesitant anti-fuzzy ideal, m-polar Q hesitant anti-fuzzy commutative ideal, m-polar Q-hesitant anti-fuzzy implicative ideal, and m-polar Q-hesitant anti-fuzzy positive implicative of BCK/BCI- algebras. In addition, we investigate several theorems, examples, and properties of these notions.
本文的主要目的是有效地定义美妙模糊集合理论中的一个新概念，即 m 极 Q-hesitant 反模糊集合，并将其应用于 BCK/BCI 对象。米极Q-hesitant反模糊集是米极模糊集与Q-hesitant模糊集结合的惊人发展。然而，我们介绍了 BCK/BCI- 代数的 m 极 Q-hesitant 反模糊子代数、m 极 Q-hesitant 反模糊理想、封闭 m 极 Q-hesitant 反模糊理想、m 极 Q 犹豫反模糊交换理想、m 极 Q-hesitant 反模糊蕴含理想和 m 极 Q-hesitant 反模糊正蕴含的知识。此外，我们还研究了这些概念的若干定理、示例和性质。
{"title":"M-polar Q-hesitant Anti-fuzzy Set in BCK/BCI-algebras","authors":"M. Alshayea, K. Alsager","doi":"10.29020/nybg.ejpam.v17i1.4952","DOIUrl":"https://doi.org/10.29020/nybg.ejpam.v17i1.4952","url":null,"abstract":"The main objective of this paper is to effectively define a new concept of the fabulous fuzzy set theory that is called m-polar Q-hesitant anti-fuzzy set and apply it to the BCK/BCI-algebras. The m-polar Q-hesitant anti-fuzzy set is an astonishing development of the combination between the m-polar fuzzy set and the Q-hesitant fuzzy set. However, we introduce knowledge of the m-polar Q-hesitant anti-fuzzy subalgebra, m-polar Q-hesitant anti-fuzzy ideal, closed m-polar Q-hesitant anti-fuzzy ideal, m-polar Q hesitant anti-fuzzy commutative ideal, m-polar Q-hesitant anti-fuzzy implicative ideal, and m-polar Q-hesitant anti-fuzzy positive implicative of BCK/BCI- algebras. In addition, we investigate several theorems, examples, and properties of these notions.","PeriodicalId":51807,"journal":{"name":"European Journal of Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140475921","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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