A Nice Separation of Some Seiffert-Type Means by Power Means
Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯. In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are more known inequalities between the means 𝒫,𝒯...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/430692 |
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| author | Iulia Costin Gheorghe Toader |
| author_facet | Iulia Costin Gheorghe Toader |
| author_sort | Iulia Costin |
| collection | DOAJ |
| description | Seiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯. In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are more known inequalities between the means 𝒫,𝒯, and ℒ and some power means 𝒜𝑝. We add to these inequalities two new results obtaining the following nice chain of inequalities 𝒜0<ℒ<𝒜1/2<𝒫<𝒜1<ℳ<𝒜3/2<𝒯<𝒜2, where the power means are evenly spaced with respect to their order. |
| format | Article |
| id | doaj-art-d9ac0ed0f243478ca478f2154f04aa28 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d9ac0ed0f243478ca478f2154f04aa282025-02-03T06:12:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252012-01-01201210.1155/2012/430692430692A Nice Separation of Some Seiffert-Type Means by Power MeansIulia Costin0Gheorghe Toader1Department of Computer Sciences, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaSeiffert has defined two well-known trigonometric means denoted by 𝒫 and 𝒯. In a similar way it was defined by Carlson the logarithmic mean ℒ as a hyperbolic mean. Neuman and Sándor completed the list of such means by another hyperbolic mean ℳ. There are more known inequalities between the means 𝒫,𝒯, and ℒ and some power means 𝒜𝑝. We add to these inequalities two new results obtaining the following nice chain of inequalities 𝒜0<ℒ<𝒜1/2<𝒫<𝒜1<ℳ<𝒜3/2<𝒯<𝒜2, where the power means are evenly spaced with respect to their order.http://dx.doi.org/10.1155/2012/430692 |
| spellingShingle | Iulia Costin Gheorghe Toader A Nice Separation of Some Seiffert-Type Means by Power Means International Journal of Mathematics and Mathematical Sciences |
| title | A Nice Separation of Some Seiffert-Type Means by Power Means |
| title_full | A Nice Separation of Some Seiffert-Type Means by Power Means |
| title_fullStr | A Nice Separation of Some Seiffert-Type Means by Power Means |
| title_full_unstemmed | A Nice Separation of Some Seiffert-Type Means by Power Means |
| title_short | A Nice Separation of Some Seiffert-Type Means by Power Means |
| title_sort | nice separation of some seiffert type means by power means |
| url | http://dx.doi.org/10.1155/2012/430692 |
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