On the p-Version of the Schwab-Borchardt Mean
This paper deals with a one-parameter generalization of the Schwab-Borchardt mean. The new mean is defined in terms of the inverse functions of the generalized trigonometric and generalized hyperbolic functions. The four new bivariate means are introduced as particular cases of the p-version of the...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2014/697643 |
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| _version_ | 1849469095287717888 |
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| author | Edward Neuman |
| author_facet | Edward Neuman |
| author_sort | Edward Neuman |
| collection | DOAJ |
| description | This paper deals with a one-parameter generalization of the Schwab-Borchardt mean. The new mean is defined in terms of the inverse functions of the generalized trigonometric and generalized hyperbolic functions. The four new bivariate means are introduced as particular cases of the p-version of the Schwab-Borchardt mean. For the particular value of the parameter p, these means become either the classical logarithmic mean or the Seiffert means or the Neuman-Sándor mean. Wilker- and Huygens-type inequalities involving inverse functions of the generalized trigonometric and the generalized hyperbolic functions are also established. |
| format | Article |
| id | doaj-art-f78fa2d80e594a23a455db2cd1a2ffad |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-f78fa2d80e594a23a455db2cd1a2ffad2025-08-20T03:25:38ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252014-01-01201410.1155/2014/697643697643On the p-Version of the Schwab-Borchardt MeanEdward Neuman0Mathematical Research Institute, 144 Hawthorn Hollow, Carbondale, IL 62903, USAThis paper deals with a one-parameter generalization of the Schwab-Borchardt mean. The new mean is defined in terms of the inverse functions of the generalized trigonometric and generalized hyperbolic functions. The four new bivariate means are introduced as particular cases of the p-version of the Schwab-Borchardt mean. For the particular value of the parameter p, these means become either the classical logarithmic mean or the Seiffert means or the Neuman-Sándor mean. Wilker- and Huygens-type inequalities involving inverse functions of the generalized trigonometric and the generalized hyperbolic functions are also established.http://dx.doi.org/10.1155/2014/697643 |
| spellingShingle | Edward Neuman On the p-Version of the Schwab-Borchardt Mean International Journal of Mathematics and Mathematical Sciences |
| title | On the p-Version of the Schwab-Borchardt Mean |
| title_full | On the p-Version of the Schwab-Borchardt Mean |
| title_fullStr | On the p-Version of the Schwab-Borchardt Mean |
| title_full_unstemmed | On the p-Version of the Schwab-Borchardt Mean |
| title_short | On the p-Version of the Schwab-Borchardt Mean |
| title_sort | on the p version of the schwab borchardt mean |
| url | http://dx.doi.org/10.1155/2014/697643 |
| work_keys_str_mv | AT edwardneuman onthepversionoftheschwabborchardtmean |