The famous Ascoli-Arzelà theorem served as a springboard for research into compactness in function spaces, particularly spaces of continuous functions. This paper investigates compact subsets of spaces of continuous functions endowed with topologies between the topology of pointwise convergence and the topology of uniform convergence. More precisely, this paper studies necessary and sufficient conditions for a subset to be compact in Cλ,u(X) for a locally-λ space X when λ ⊇ 𝓕(X), for a hemi-λλf-space X when λ ⊆ 𝓟 𝓢(X), and for a k-space X when λ ⊇ 𝓚(X). This paper also studies that every bounded subset of Cλ,u(X) has compact closure for some classes of topological spaces X.
著名的阿斯科利-阿尔泽拉定理是研究函数空间（尤其是连续函数空间）紧凑性的跳板。本文研究连续函数空间的紧凑子集，其拓扑介于点收敛拓扑和均匀收敛拓扑之间。更确切地说，对于局部-λ空间 X（当λ⊇ 𝓕(X)时），对于半λf -空间 X（当λ ⊆ 𝓟 𝓢(X)时），以及对于 k 空间 X（当λ⊇ 𝓚(X)时），本文研究了子集在 C λ,u (X) 中紧凑的必要条件和充分条件。本文还研究了对于某些类别的拓扑空间 X，C λ,u (X) 的每个有界子集都有紧凑闭包。
{"title":"Compact subsets of C λ,u (X)","authors":"Prashant Kumar, Pratibha Garg","doi":"10.1515/ms-2024-0012","DOIUrl":"https://doi.org/10.1515/ms-2024-0012","url":null,"abstract":"The famous Ascoli-Arzelà theorem served as a springboard for research into compactness in function spaces, particularly spaces of continuous functions. This paper investigates compact subsets of spaces of continuous functions endowed with topologies between the topology of pointwise convergence and the topology of uniform convergence. More precisely, this paper studies necessary and sufficient conditions for a subset to be compact in <jats:italic>C</jats:italic> <jats:sub> <jats:italic>λ</jats:italic>,<jats:italic>u</jats:italic> </jats:sub>(<jats:italic>X</jats:italic>) for a locally-<jats:italic>λ</jats:italic> space <jats:italic>X</jats:italic> when <jats:italic>λ</jats:italic> ⊇ 𝓕(<jats:italic>X</jats:italic>), for a hemi-<jats:overline> <jats:italic>λ</jats:italic> </jats:overline> <jats:italic>λ<jats:sub>f</jats:sub> </jats:italic>-space <jats:italic>X</jats:italic> when <jats:italic>λ</jats:italic> ⊆ 𝓟 𝓢(<jats:italic>X</jats:italic>), and for a <jats:italic>k</jats:italic>-space <jats:italic>X</jats:italic> when <jats:italic>λ</jats:italic> ⊇ 𝓚(<jats:italic>X</jats:italic>). This paper also studies that every bounded subset of <jats:italic>C</jats:italic> <jats:sub> <jats:italic>λ</jats:italic>,<jats:italic>u</jats:italic> </jats:sub>(<jats:italic>X</jats:italic>) has compact closure for some classes of topological spaces <jats:italic>X</jats:italic>.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168608","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}
Related to generalized arithmetic triangle, we introduce the hyper (r, q)-Fibonacci polynomials as the sum of these elements along a finite ray starting from a specific point, which generalize the hyper-Fibonacci polynomials. We give generating function, recurrence relations and we show some properties whose application allows us to extend the notion of Cassini determinant and to study some ratios. Moreover, we derive a connection between these polynomials and the incomplete (r, q)-Fibonacci polynomials defined in this paper.
{"title":"On hyper (r, q)-Fibonacci polynomials","authors":"Hacéne Belbachir, Fariza Krim","doi":"10.1515/ms-2024-0002","DOIUrl":"https://doi.org/10.1515/ms-2024-0002","url":null,"abstract":"Related to generalized arithmetic triangle, we introduce the hyper (<jats:italic>r</jats:italic>, <jats:italic>q</jats:italic>)-Fibonacci polynomials as the sum of these elements along a finite ray starting from a specific point, which generalize the hyper-Fibonacci polynomials. We give generating function, recurrence relations and we show some properties whose application allows us to extend the notion of Cassini determinant and to study some ratios. Moreover, we derive a connection between these polynomials and the incomplete (<jats:italic>r</jats:italic>, <jats:italic>q</jats:italic>)-Fibonacci polynomials defined in this paper.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168636","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 Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function’s radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones.
{"title":"Certain radii problems for 𝓢∗(ψ) and special functions","authors":"Kamaljeet Gangania, S. Sivaprasad Kumar","doi":"10.1515/ms-2024-0006","DOIUrl":"https://doi.org/10.1515/ms-2024-0006","url":null,"abstract":"In Geometric function theory, the Ma-Minda class of starlike functions has a unique place as it unifies various subclasses of starlike functions. There has been an vivid interplay between special functions and their geometric properties, like starlikeness. In this article, we establish certain special function’s radius of Ma-Minda starlikness. As an application, we obtain conditions on parameters for these special functions to be in the Ma-Minda class. Further, we focus on certain convolution properties for the Ma-Minda class that are not done so far, and study their applications in radius problem. Finally, we prove a variational problem of Goluzin, namely, the region of variability for the Ma-Minda class. Our results simplify and generalize the already-known ones.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168458","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}
Given a continuum X, Cn(X) denotes the hyperspace of nonempty closed subsets of X with at most n components. A strong size level is a subset of the form σ−1(t), where σ is a strong size map for Cn(X) and t ∈ (0, 1]. In this paper, answering a question by Capulín-Pérez, Fuentes-Montes de Oca, Lara-Mejía and Orozco-Zitli, we prove that for each n ≥ 2, no strong size level for Cn(X) is irreducible.
给定一个连续体 X，Cn (X) 表示最多有 n 个分量的 X 的非空封闭子集的超空间。强大小层是形式为 σ -1(t) 的子集，其中 σ 是 Cn (X) 的强大小映射，t∈ (0, 1]。在本文中，为了回答 Capulín-Pérez、Fuentes-Montes de Oca、Lara-Mejía 和 Orozco-Zitli 提出的问题，我们证明了对于每个 n ≥ 2，Cn (X) 的强大小层次都是不可还原的。
{"title":"Irreducibility of strong size levels","authors":"Alejandro Illanes, Verónica Martínez-de-la-Vega","doi":"10.1515/ms-2024-0039","DOIUrl":"https://doi.org/10.1515/ms-2024-0039","url":null,"abstract":"Given a continuum <jats:italic>X</jats:italic>, <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) denotes the hyperspace of nonempty closed subsets of <jats:italic>X</jats:italic> with at most <jats:italic>n</jats:italic> components. A strong size level is a subset of the form <jats:italic>σ</jats:italic> <jats:sup>−1</jats:sup>(<jats:italic>t</jats:italic>), where <jats:italic>σ</jats:italic> is a strong size map for <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) and <jats:italic>t</jats:italic> ∈ (0, 1]. In this paper, answering a question by Capulín-Pérez, Fuentes-Montes de Oca, Lara-Mejía and Orozco-Zitli, we prove that for each <jats:italic>n</jats:italic> ≥ 2, no strong size level for <jats:italic>C<jats:sub>n</jats:sub> </jats:italic>(<jats:italic>X</jats:italic>) is irreducible.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141170129","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}
ABSTRACT The generalization of the family of distributions that could provide a simple, and efficient algorithm for parameter estimation and study of the behavior of datasets from various fields has received significant interest. Such a model has enormous advantages, such as its flexible nature, and the regression form can easily be derived. In the literature, various generalized families of distributions have been introduced. Despite the merits of these distributions, they still have some limitations due to many parameters in the model. Thus, the estimation of parameters often becomes cumbersome. Therefore, this study introduced the alpha power Muth or Teissier-G family of continuous distributions with well-defined parameters, and obtained the joint progressive type-II censoring scheme and their reliability measures. Furthermore, we obtained the global and local influences of the APTG model. We used real-life and simulated data to evaluate the numerical applications of the introduced model. The results show that the alpha power Muth or Teissier-G family of distributions gave the best fits to both datasets than some existing models.
摘要 对分布系列进行概括，为参数估计和研究各领域数据集的行为提供一种简单而有效的算法，已引起人们的极大兴趣。这种模型具有极大的优势，如其灵活的性质和易于导出的回归形式。文献中介绍了各种广义的分布系列。尽管这些分布有其优点，但由于模型中的参数较多，它们仍有一些局限性。因此，参数估计往往变得繁琐。因此，本研究引入了具有明确参数的连续分布的 alpha power Muth 或 Teissier-G 系列，并获得了联合渐进式 II 型普查方案及其可靠性度量。此外，我们还获得了 APTG 模型的全局和局部影响因素。我们利用实际数据和模拟数据对所引入模型的数值应用进行了评估。结果表明，与现有的一些模型相比，α幂 Muth 或 Teissier-G 系列分布对两个数据集的拟合效果最好。
{"title":"The Alpha Power Muth-G Distributions and Its Applications in Survival and Reliability Analyses","authors":"J. T. Eghwerido, Ikechukwu Friday Agu","doi":"10.1515/ms-2023-0116","DOIUrl":"https://doi.org/10.1515/ms-2023-0116","url":null,"abstract":"ABSTRACT The generalization of the family of distributions that could provide a simple, and efficient algorithm for parameter estimation and study of the behavior of datasets from various fields has received significant interest. Such a model has enormous advantages, such as its flexible nature, and the regression form can easily be derived. In the literature, various generalized families of distributions have been introduced. Despite the merits of these distributions, they still have some limitations due to many parameters in the model. Thus, the estimation of parameters often becomes cumbersome. Therefore, this study introduced the alpha power Muth or Teissier-G family of continuous distributions with well-defined parameters, and obtained the joint progressive type-II censoring scheme and their reliability measures. Furthermore, we obtained the global and local influences of the APTG model. We used real-life and simulated data to evaluate the numerical applications of the introduced model. The results show that the alpha power Muth or Teissier-G family of distributions gave the best fits to both datasets than some existing models.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138988194","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}
ABSTRACT In this work, we study the integration of the differential-difference sine-Gordon equation with an integral type source. We deduce the time performance of the scattering data of the spectral problem which is associated with the discrete sine-Gordon equation. Using the inverse scattering method, we integrate the Cauchy problem for the differential-difference sine-Gordon equation with the integral type source in the class of the rapidly decreasing functions.
{"title":"On the Differential-Difference Sine-Gordon Equation with an Integral Type Source","authors":"B. Babajanov, Michal Fečkan, Aygul Babadjanova","doi":"10.1515/ms-2023-0108","DOIUrl":"https://doi.org/10.1515/ms-2023-0108","url":null,"abstract":"ABSTRACT In this work, we study the integration of the differential-difference sine-Gordon equation with an integral type source. We deduce the time performance of the scattering data of the spectral problem which is associated with the discrete sine-Gordon equation. Using the inverse scattering method, we integrate the Cauchy problem for the differential-difference sine-Gordon equation with the integral type source in the class of the rapidly decreasing functions.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139017636","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}
ABSTRACT We establish explicit constructions of real transcendental numbers that are not U-numbers with respect to Mahler’s classification by using regular continued fraction expansions of irrational real algebraic numbers.
摘要 我们利用无理实代数数的正则续分展开，建立了实超验数的显式构造，这些实超验数在马勒的分类中不是 U 数。
{"title":"On Transcendental Regular Continued Fractions","authors":"Gülcan Kekeç","doi":"10.1515/ms-2023-0101","DOIUrl":"https://doi.org/10.1515/ms-2023-0101","url":null,"abstract":"ABSTRACT We establish explicit constructions of real transcendental numbers that are not U-numbers with respect to Mahler’s classification by using regular continued fraction expansions of irrational real algebraic numbers.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139024313","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}
ABSTRACT In this paper, we introduce the notion of generalized anti-symmetry laws in groupoids, and we apply this concept to several algebraic structures. Moreover, we show that every Fibonacci sequence on (C, *) is periodic.
{"title":"Generalized Anti-Symmetry Laws in Groupoids","authors":"Sun Shin Ahn, Hee Sik Kim, Young Joo Seo","doi":"10.1515/ms-2023-0104","DOIUrl":"https://doi.org/10.1515/ms-2023-0104","url":null,"abstract":"ABSTRACT In this paper, we introduce the notion of generalized anti-symmetry laws in groupoids, and we apply this concept to several algebraic structures. Moreover, we show that every Fibonacci sequence on (C, *) is periodic.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138991806","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}
ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being addressed through this paper. The class in question consists of uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms, and the results presented here are a natural continuation and extension of some previous works with an emphasis on a much wider class of uninorms as inner operators.
{"title":"Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm","authors":"D. Jocic, I. Štajner-Papuga","doi":"10.1515/ms-2023-0110","DOIUrl":"https://doi.org/10.1515/ms-2023-0110","url":null,"abstract":"ABSTRACT The issue of distributivity of aggregation operators is crucial for many different areas such as fuzzy sets and fuzzy logic, pseudo-analysis and measure theory, and particulary in the decision making theory. The problem of distributivity of an operator form a special class of uni-nullnorms over a general uninorm is being addressed through this paper. The class in question consists of uni-nullnorms with continuous and Archimedean underlying t-norms and t-conorms, and the results presented here are a natural continuation and extension of some previous works with an emphasis on a much wider class of uninorms as inner operators.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139013656","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}
ABSTRACT It is known that the Golden space form may not be an Einstein manifold. In this paper, it is shown that the condition to be Einstein for a Golden space form is equivalent to being weakly Einstein. In addition, the partial geodesic and cyclic parallelism of the CR-submanifolds of a Golden space are examined, and the case of the constant Golden sectional curvature is determined. Moreover, the CR-submanifolds with semi-flat normal connection are studied and an inequality is obtained. The equality case of this inequality is also checked. We also consider the totally umbilical CR-submanifold of Golden Riemannian manifolds and show that such submanifolds are totally geodesic under certain conditions. Furthermore, we obtain an inequality involving the scalar curvature of CR-submanifold and check the existence of extrinsic spheres in Golden space forms.
{"title":"Weakly Einstein Equivalence in a Golden Space Form and Certain CR-submanifolds","authors":"Jihun Kim, Jeonghyeong Park, Bayram Şahin","doi":"10.1515/ms-2023-0117","DOIUrl":"https://doi.org/10.1515/ms-2023-0117","url":null,"abstract":"ABSTRACT It is known that the Golden space form may not be an Einstein manifold. In this paper, it is shown that the condition to be Einstein for a Golden space form is equivalent to being weakly Einstein. In addition, the partial geodesic and cyclic parallelism of the CR-submanifolds of a Golden space are examined, and the case of the constant Golden sectional curvature is determined. Moreover, the CR-submanifolds with semi-flat normal connection are studied and an inequality is obtained. The equality case of this inequality is also checked. We also consider the totally umbilical CR-submanifold of Golden Riemannian manifolds and show that such submanifolds are totally geodesic under certain conditions. Furthermore, we obtain an inequality involving the scalar curvature of CR-submanifold and check the existence of extrinsic spheres in Golden space forms.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139021638","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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