Comparing weighted densities
Abstract In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on the asymptotic relation between the weight functions, we give sharp bounds for possible values of one density when the values of another densit...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02885-y |
| _version_ | 1811303735559716864 |
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| author | József Bukor Ferdinánd Filip Jan Šustek János T. Tóth |
| author_facet | József Bukor Ferdinánd Filip Jan Šustek János T. Tóth |
| author_sort | József Bukor |
| collection | DOAJ |
| description | Abstract In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on the asymptotic relation between the weight functions, we give sharp bounds for possible values of one density when the values of another density are given. In particular, we give a condition for two weight functions to generate equivalent weighted densities. |
| first_indexed | 2024-04-13T07:52:12Z |
| format | Article |
| id | doaj.art-39942ac2aaa54a6983f643ed06144f1f |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-13T07:52:12Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-39942ac2aaa54a6983f643ed06144f1f2022-12-22T02:55:29ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-11-012022112010.1186/s13660-022-02885-yComparing weighted densitiesJózsef Bukor0Ferdinánd Filip1Jan Šustek2János T. Tóth3J. Selye UniversityJ. Selye UniversityUniversity of OstravaJ. Selye UniversityAbstract In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on the asymptotic relation between the weight functions, we give sharp bounds for possible values of one density when the values of another density are given. In particular, we give a condition for two weight functions to generate equivalent weighted densities.https://doi.org/10.1186/s13660-022-02885-yAsymptotic densityLogarithmic densityWeighted density |
| spellingShingle | József Bukor Ferdinánd Filip Jan Šustek János T. Tóth Comparing weighted densities Journal of Inequalities and Applications Asymptotic density Logarithmic density Weighted density |
| title | Comparing weighted densities |
| title_full | Comparing weighted densities |
| title_fullStr | Comparing weighted densities |
| title_full_unstemmed | Comparing weighted densities |
| title_short | Comparing weighted densities |
| title_sort | comparing weighted densities |
| topic | Asymptotic density Logarithmic density Weighted density |
| url | https://doi.org/10.1186/s13660-022-02885-y |
| work_keys_str_mv | AT jozsefbukor comparingweighteddensities AT ferdinandfilip comparingweighteddensities AT jansustek comparingweighteddensities AT janosttoth comparingweighteddensities |