Pub Date : 2022-05-30DOI: 10.12697/acutm.2022.26.08
Torkia Ben Jmaa, A. Makhlouf, N. Saadaoui
In this paper, we study Hom-Lie structures on tensor products. In particular, we consider current Hom-Lie algebras and discuss their representations. We determine faithful representations of minimal dimension of current Heisenberg Hom-Lie algebras. Moreover derivations, including generalized derivations, and centroids are studied. Furthermore, cohomology and extensions of current Hom-Lie algebras are also considered.
{"title":"Current Hom-Lie algebras","authors":"Torkia Ben Jmaa, A. Makhlouf, N. Saadaoui","doi":"10.12697/acutm.2022.26.08","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.08","url":null,"abstract":"In this paper, we study Hom-Lie structures on tensor products. In particular, we consider current Hom-Lie algebras and discuss their representations. We determine faithful representations of minimal dimension of current Heisenberg Hom-Lie algebras. Moreover derivations, including generalized derivations, and centroids are studied. Furthermore, cohomology and extensions of current Hom-Lie algebras are also considered.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75941991","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 : 2022-05-30DOI: 10.12697/acutm.2022.26.09
D. Behloul, Akila Djoumakh, Lyes Ait-Amrane
In this paper, we present new identities involving the biperiodic Fibonacci and Lucas sequences. Then we solve completely some quadratic Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences.
{"title":"Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences","authors":"D. Behloul, Akila Djoumakh, Lyes Ait-Amrane","doi":"10.12697/acutm.2022.26.09","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.09","url":null,"abstract":"In this paper, we present new identities involving the biperiodic Fibonacci and Lucas sequences. Then we solve completely some quadratic Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83067775","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 : 2022-05-28DOI: 10.12697/acutm.2022.26.02
A. Wanas, B. Frasin, S. R. Swamy, Y. Sailaja
In the present paper, we determine upper bounds for the first two Taylor–Maclaurin coefficients |a2| and |a3| for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete–Szegö problem of functions belonging to this family. Further, we point out several special cases of our results.
{"title":"Coefficients bounds for a family of bi-univalent functions defined by Horadam polynomials","authors":"A. Wanas, B. Frasin, S. R. Swamy, Y. Sailaja","doi":"10.12697/acutm.2022.26.02","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.02","url":null,"abstract":"In the present paper, we determine upper bounds for the first two Taylor–Maclaurin coefficients |a2| and |a3| for a certain family of holomorphic and bi-univalent functions defined by using the Horadam polynomials. Also, we solve Fekete–Szegö problem of functions belonging to this family. Further, we point out several special cases of our results.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72374361","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 : 2022-05-28DOI: 10.12697/acutm.2022.26.03
E. Özkan, B. Kuloğlu
We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers.
{"title":"On the bicomplex Gaussian Fibonacci and Gaussian Lucas numbers","authors":"E. Özkan, B. Kuloğlu","doi":"10.12697/acutm.2022.26.03","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.03","url":null,"abstract":"We give the bicomplex Gaussian Fibonacci and the bicomplex Gaussian Lucas numbers and establish the generating functions and Binet’s formulas related to these numbers. Also, we present the summation formula, matrix representation and Honsberger identity and their relationship between these numbers. Finally, we show the relationships among the bicomplex Gaussian Fibonacci, the bicomplex Gaussian Lucas, Gaussian Fibonacci, Gaussian Lucas and Fibonacci numbers.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75402493","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 : 2022-05-27DOI: 10.12697/acutm.2022.26.01
A. Banerjee, A. Kundu
We study the uniqueness problem of two special classes of meromorphic functions sharing two sets of small functions. One of the considered classes has the property to include the Selberg class L functions, while the other class is comprising of arbitrary meromorphic functions having finitely many poles. We obtain a number of results which extend and improve a number of earlier results such as Li [ Proc. Amer. Math. Soc., 138 (2010), 2071-2077], Lin and Lin [Filomat 30 (2016), 3795-3806] and others. We have also been able to replace the strict CM (IM) sharing of the sets in our theorems to almost CM (almost IM) sharing.
{"title":"On the uniqueness of two different classes of meromorphic functions under the sharing of two sets of rational functions","authors":"A. Banerjee, A. Kundu","doi":"10.12697/acutm.2022.26.01","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.01","url":null,"abstract":"We study the uniqueness problem of two special classes of meromorphic functions sharing two sets of small functions. One of the considered classes has the property to include the Selberg class L functions, while the other class is comprising of arbitrary meromorphic functions having finitely many poles. We obtain a number of results which extend and improve a number of earlier results such as Li [ Proc. Amer. Math. Soc., 138 (2010), 2071-2077], Lin and Lin [Filomat 30 (2016), 3795-3806] and others. We have also been able to replace the strict CM (IM) sharing of the sets in our theorems to almost CM (almost IM) sharing. ","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76334731","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 : 2022-05-27DOI: 10.12697/acutm.2022.26.11
M. Vikerpuur, Margus Lillemäe, A. Pedas
We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.
{"title":"Central part interpolation schemes for a class of fractional initial value problems","authors":"M. Vikerpuur, Margus Lillemäe, A. Pedas","doi":"10.12697/acutm.2022.26.11","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.11","url":null,"abstract":"We consider an initial value problem for linear fractional integro-differential equations with weakly singular kernels. Using an integral equation reformulation of the underlying problem, a collocation method based on the central part interpolation by continuous piecewise polynomials on the uniform grid is constructed and analysed. Optimal convergence order of the proposed method is established and confirmed by numerical experiments.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73776998","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 : 2022-05-27DOI: 10.12697/acutm.2022.26.10
M. Abel
We show that if (A, f, B) and (B, g, C) are left (right or two-sided) Segal topological algebras for which g(f(A))⊆ g(B)g(f(A)) (g(f(A))⊆ g(f(A))g(B) or g(f(A))⊆ g(B)g(f(A))∩ g(f(A))g(B), respectively), then (A, g∘ f, C) is also a left (right or two-sided, respectively) Segal topological algebra.
我们表明,如果(f, B)和(B、g、C)左(右、双边)Segal拓扑代数的g (f (A))⊆g (B) g (f (A)) (g (f (A))⊆g (f (A)) g (B)或g (f (A))⊆g (B) g (f (A))∩g (f (A)) g (B),分别),然后(g∘f C)也是一个左(右或两面分别)Segal拓扑代数。
{"title":"About the transitivity of the property of being Segal topological algebra","authors":"M. Abel","doi":"10.12697/acutm.2022.26.10","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.10","url":null,"abstract":"We show that if (A, f, B) and (B, g, C) are left (right or two-sided) Segal topological algebras for which g(f(A))⊆ g(B)g(f(A)) (g(f(A))⊆ g(f(A))g(B) or g(f(A))⊆ g(B)g(f(A))∩ g(f(A))g(B), respectively), then (A, g∘ f, C) is also a left (right or two-sided, respectively) Segal topological algebra.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2022-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83870427","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 : 2021-11-19DOI: 10.12697/acutm.2022.26.07
R. Haller, Nikita Leo, O. Zavarzina
We prove that Banach spaces ℓ1 ⊕2 R and X ⊕∞ Y , with strictly convex X and Y , have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).
{"title":"Two new examples of Banach spaces with a plastic unit ball","authors":"R. Haller, Nikita Leo, O. Zavarzina","doi":"10.12697/acutm.2022.26.07","DOIUrl":"https://doi.org/10.12697/acutm.2022.26.07","url":null,"abstract":"We prove that Banach spaces ℓ1 ⊕2 R and X ⊕∞ Y , with strictly convex X and Y , have plastic unit balls (we call a metric space plastic if every non-expansive bijection from this space onto itself is an isometry).","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79290795","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.12
H. Dutta, Jyotishmaan Gogoi
We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results.
{"title":"Tauberian theorems for weighted mean statistical summability of double sequences of fuzzy numbers","authors":"H. Dutta, Jyotishmaan Gogoi","doi":"10.12697/acutm.2021.25.12","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.12","url":null,"abstract":"We discuss Tauberian conditions under which the statistical convergence of double sequences of fuzzy numbers follows from the statistical convergence of their weighted means. We also prove some other results which are necessary to establish the main results.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86850567","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 : 2021-11-17DOI: 10.12697/acutm.2021.25.18
K. Ho
This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.
本文建立了混合范数空间的外推理论。利用这一外推理论，我们得到了Rubio de Francia Littlewood-Paley函数和几何极大函数在混合范数空间上的映射性质。作为这些结果的特例，我们得到了变指数混合范数Lebesgue空间和混合范数Lorentz空间上的映射性质。
{"title":"Extrapolation to mixed norm spaces and applications","authors":"K. Ho","doi":"10.12697/acutm.2021.25.18","DOIUrl":"https://doi.org/10.12697/acutm.2021.25.18","url":null,"abstract":"This paper establishes extrapolation theory to mixed norm spaces. By applying this extrapolation theory, we obtain the mapping properties of the Rubio de Francia Littlewood-Paley functions and the geometrical maximal functions on mixed norm spaces. As special cases of these results, we have the mapping properties on the mixed norm Lebesgue spaces with variable exponents and the mixed norm Lorentz spaces.","PeriodicalId":42426,"journal":{"name":"Acta et Commentationes Universitatis Tartuensis de Mathematica","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2021-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85971946","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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