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Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags 具有时变滞后的非线性分式中性混合微分方程的一些新的唯一性和乌拉姆-赫尔斯型稳定性结果
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0029
Nguyen Minh Dien
{"title":"Some new uniqueness and Ulam–Hyers type stability results for nonlinear fractional neutral hybrid differential equations with time-varying lags","authors":"Nguyen Minh Dien","doi":"10.1515/ms-2024-0029","DOIUrl":"https://doi.org/10.1515/ms-2024-0029","url":null,"abstract":"This paper deals with some qualitative properties of solutions to nonlinear neutral hybrid differential equations connected to <jats:italic>ψ</jats:italic>-Caputo fractional derivative with time-varying lags. First, we demonstrate the problem possesses a mild solution uniquely where the source function may have temporal singularities. Second, in some cases, we indicate that the problem possesses a unique mild solution under some weaker conditions than the previous one. Third, we also obtain a result on a global mild solution for the problem. Finally, the results are further enriched by studying a new type of Ulam–Hyers stability for the main equation. The main results are obtained by applying the nice inequality, first proposed and proven in this paper. Some befit examples are given to justify the applicability of the main results.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"17 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168521","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}
引用次数: 0
Compact subsets of C λ,u (X) C λ,u (X) 的紧凑子集
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0012
Prashant Kumar, Pratibha Garg
{"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":"69 1","pages":""},"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}
引用次数: 0
On hyper (r, q)-Fibonacci polynomials 关于超（r，q）-斐波那契多项式
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0002
Hacéne Belbachir, Fariza Krim
{"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":"51 1","pages":""},"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}
引用次数: 0
Irreducibility of strong size levels 强尺寸等级的不可还原性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2024-05-28 DOI: 10.1515/ms-2024-0039
Alejandro Illanes, Verónica Martínez-de-la-Vega
{"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":"63 1","pages":""},"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}
引用次数: 0
The Alpha Power Muth-G Distributions and Its Applications in Survival and Reliability Analyses 阿尔法幂 Muth-G 分布及其在生存和可靠性分析中的应用
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2023-12-01 DOI: 10.1515/ms-2023-0116
J. T. Eghwerido, Ikechukwu Friday Agu
{"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":"130 3","pages":"1597 - 1614"},"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}
引用次数: 0
On the Differential-Difference Sine-Gordon Equation with an Integral Type Source 关于带有积分型源的微分-差分正弦-戈登方程
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2023-12-01 DOI: 10.1515/ms-2023-0108
B. Babajanov, Michal Fečkan, Aygul Babadjanova
{"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":"38 9","pages":"1499 - 1510"},"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}
引用次数: 0
On Transcendental Regular Continued Fractions 论超越正则连续分数
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2023-12-01 DOI: 10.1515/ms-2023-0101
Gülcan Kekeç
{"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":"93 2","pages":"1399 - 1408"},"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}
引用次数: 0
Generalized Anti-Symmetry Laws in Groupoids 类群中的广义反对称律
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2023-12-01 DOI: 10.1515/ms-2023-0104
Sun Shin Ahn, Hee Sik Kim, Young Joo Seo
{"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":"259 ","pages":"1435 - 1444"},"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}
引用次数: 0
Distributivity of a Uni-nullnorm with Continuous and Archimedean Underlying T-norms and T-conorms Over an Arbitrary Uninorm 具有连续和阿基米德基础 T-norms 和 T-conorms 的 Uni-nullnorm 在任意 Uninorm 上的可分配性
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2023-12-01 DOI: 10.1515/ms-2023-0110
D. Jocic, I. Štajner-Papuga
{"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":"151 ","pages":"1527 - 1544"},"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}
引用次数: 0
Operators that are Weakly Coercive and a Compact Perturbation 弱强制算子和紧凑扰动
IF 1.6 3区 数学
Mathematica Slovaca Pub Date : 2023-12-01 DOI: 10.1515/ms-2023-0112
J. M. Soriano Arbizu, Manuel Ordoñez Cabrera
{"title":"Operators that are Weakly Coercive and a Compact Perturbation","authors":"J. M. Soriano Arbizu, Manuel Ordoñez Cabrera","doi":"10.1515/ms-2023-0112","DOIUrl":"https://doi.org/10.1515/ms-2023-0112","url":null,"abstract":"ABSTRACT Let X, Y be two Banach spaces over K=ℝ [mathbb{K}=mathbb{R}] or ℂ [mathbb{C}] , and let f := F+C be a weakly coercive operator from X onto Y, where F is a Fredholm proper operator, and C is a C1-compact operator. Sufficient conditions are provided to assert that the perturbed operator f is a C1-diffeomorphism. When one of these conditions does not hold and instead y is a regular value, the equation f(x) = y has at most finite number of solutions. As a consequence of the main result two corollaries are given. A second theorem studies the finite dimensional case. As an application, one example is given. The proof of our results is based on properties of Fredholm operators, as well as on local and global inverse mapping theorems.","PeriodicalId":18282,"journal":{"name":"Mathematica Slovaca","volume":"269 ","pages":"1559 - 1568"},"PeriodicalIF":1.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138991853","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}
引用次数: 0
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