Some special cases on Stolarsky’s means
In this paper we observe that one-parameter Stolarsky’s means (SM) are deduced from both the Mean Value Theorem for derivatives (MVTD) and the Mean Value Theorem for definite integrals (MVTI), and we study their elementary properties as the parameter varies. In the subfamily of SM having a natural n...
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Accademia Piceno Aprutina dei Velati
2024-12-01
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| Series: | Ratio Mathematica |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1637 |
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| author | Cesare Palmisani |
| author_facet | Cesare Palmisani |
| author_sort | Cesare Palmisani |
| collection | DOAJ |
| description | In this paper we observe that one-parameter Stolarsky’s means (SM) are deduced from both the Mean Value Theorem for derivatives (MVTD) and the Mean Value Theorem for definite integrals (MVTI), and we study their elementary properties as the parameter varies. In the subfamily of SM having a natural number as parameter, we geometrically interpret one of them in particular as a real elliptic cone. We link SM having the integer power of a prime number as a parameter to classical means (i.e., harmonic mean, geometric mean, arithmetic mean, power mean). Finally, from an extension of Flett's Theorem (FT), we derive the expression of a new mean that is a upper bound of the arithmetic mean. |
| format | Article |
| id | doaj-art-f06ebf887dda46eaaa8da2cb70cb731b |
| institution | Kabale University |
| issn | 1592-7415 2282-8214 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj-art-f06ebf887dda46eaaa8da2cb70cb731b2025-02-01T06:51:01ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142024-12-0153010.23755/rm.v53i0.1637954Some special cases on Stolarsky’s meansCesare Palmisani0* Department of Political Sciences – Federico II; Naples; cpalmisani@unina.it.In this paper we observe that one-parameter Stolarsky’s means (SM) are deduced from both the Mean Value Theorem for derivatives (MVTD) and the Mean Value Theorem for definite integrals (MVTI), and we study their elementary properties as the parameter varies. In the subfamily of SM having a natural number as parameter, we geometrically interpret one of them in particular as a real elliptic cone. We link SM having the integer power of a prime number as a parameter to classical means (i.e., harmonic mean, geometric mean, arithmetic mean, power mean). Finally, from an extension of Flett's Theorem (FT), we derive the expression of a new mean that is a upper bound of the arithmetic mean.http://eiris.it/ojs/index.php/ratiomathematica/article/view/1637 |
| spellingShingle | Cesare Palmisani Some special cases on Stolarsky’s means Ratio Mathematica |
| title | Some special cases on Stolarsky’s means |
| title_full | Some special cases on Stolarsky’s means |
| title_fullStr | Some special cases on Stolarsky’s means |
| title_full_unstemmed | Some special cases on Stolarsky’s means |
| title_short | Some special cases on Stolarsky’s means |
| title_sort | some special cases on stolarsky s means |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/1637 |
| work_keys_str_mv | AT cesarepalmisani somespecialcasesonstolarskysmeans |