A new analogue of Gauss' functional equation
Gauss established a theory on the functional equation (Gauss' functional equation) f(a+b2,ab)=f(a,b) (a,b>0), where f:R+×R+→R is an unknown function of the above equation.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000962 |
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| _version_ | 1832565141634285568 |
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| author | Hiroshi Haruki Themistocles M. Rassias |
| author_facet | Hiroshi Haruki Themistocles M. Rassias |
| author_sort | Hiroshi Haruki |
| collection | DOAJ |
| description | Gauss established a theory on the functional equation (Gauss' functional equation)
f(a+b2,ab)=f(a,b) (a,b>0),
where f:R+×R+→R is an unknown function of the above equation. |
| format | Article |
| id | doaj-art-0a88c9ce26f14e2798fec545b0a1f9be |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0a88c9ce26f14e2798fec545b0a1f9be2025-02-03T01:09:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118474975610.1155/S0161171295000962A new analogue of Gauss' functional equationHiroshi Haruki0Themistocles M. Rassias1Department of Pure Mathematics, Faculty of Mathematics, University of Waterloo, Ontario, Waterloo N2L 3G1, CanadaDepartment of Mathematics, University of La Verne, P.O. Box 51105, Kifissia, Athens 14510, GreeceGauss established a theory on the functional equation (Gauss' functional equation) f(a+b2,ab)=f(a,b) (a,b>0), where f:R+×R+→R is an unknown function of the above equation.http://dx.doi.org/10.1155/S0161171295000962Gauss' functional equationthe arithmetic-geometric mean of Gaussthe arithmetic-harmonic mean. |
| spellingShingle | Hiroshi Haruki Themistocles M. Rassias A new analogue of Gauss' functional equation International Journal of Mathematics and Mathematical Sciences Gauss' functional equation the arithmetic-geometric mean of Gauss the arithmetic-harmonic mean. |
| title | A new analogue of Gauss' functional equation |
| title_full | A new analogue of Gauss' functional equation |
| title_fullStr | A new analogue of Gauss' functional equation |
| title_full_unstemmed | A new analogue of Gauss' functional equation |
| title_short | A new analogue of Gauss' functional equation |
| title_sort | new analogue of gauss functional equation |
| topic | Gauss' functional equation the arithmetic-geometric mean of Gauss the arithmetic-harmonic mean. |
| url | http://dx.doi.org/10.1155/S0161171295000962 |
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