On the Superstability Related with the Trigonometric Functional Equation
We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x+y)±g(x−y)=λf(x)g(y), f(x+y)±g(x−y)=λg(x)f(y), f(x+y)±g(x−y)=λf(...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://dx.doi.org/10.1155/2009/503724 |
| _version_ | 1811251572204634112 |
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| author | Gwang Hui Kim |
| author_facet | Gwang Hui Kim |
| author_sort | Gwang Hui Kim |
| collection | DOAJ |
| description | We will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x+y)±g(x−y)=λf(x)g(y), f(x+y)±g(x−y)=λg(x)f(y), f(x+y)±g(x−y)=λf(x)f(y), f(x+y)±g(x−y)=λg(x)g(y), which can be considered the mixed functional equations of the sine function and cosine function, of the hyperbolic sine function and hyperbolic cosine function, and of the exponential functions, respectively. |
| first_indexed | 2024-04-12T16:22:26Z |
| format | Article |
| id | doaj.art-f3844e7855c14fedb307283c3effccaf |
| institution | Directory Open Access Journal |
| issn | 1687-1839 1687-1847 |
| language | English |
| last_indexed | 2024-04-12T16:22:26Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-f3844e7855c14fedb307283c3effccaf2022-12-22T03:25:32ZengSpringerOpenAdvances in Difference Equations1687-18391687-18472009-01-01200910.1155/2009/503724On the Superstability Related with the Trigonometric Functional EquationGwang Hui KimWe will investigate the superstability of the (hyperbolic) trigonometric functional equation from the following functional equations: f(x+y)±g(x−y)=λf(x)g(y), f(x+y)±g(x−y)=λg(x)f(y), f(x+y)±g(x−y)=λf(x)f(y), f(x+y)±g(x−y)=λg(x)g(y), which can be considered the mixed functional equations of the sine function and cosine function, of the hyperbolic sine function and hyperbolic cosine function, and of the exponential functions, respectively.http://dx.doi.org/10.1155/2009/503724 |
| spellingShingle | Gwang Hui Kim On the Superstability Related with the Trigonometric Functional Equation Advances in Difference Equations |
| title | On the Superstability Related with the Trigonometric Functional Equation |
| title_full | On the Superstability Related with the Trigonometric Functional Equation |
| title_fullStr | On the Superstability Related with the Trigonometric Functional Equation |
| title_full_unstemmed | On the Superstability Related with the Trigonometric Functional Equation |
| title_short | On the Superstability Related with the Trigonometric Functional Equation |
| title_sort | on the superstability related with the trigonometric functional equation |
| url | http://dx.doi.org/10.1155/2009/503724 |
| work_keys_str_mv | AT gwanghuikim onthesuperstabilityrelatedwiththetrigonometricfunctionalequation |