On the Hyers-Ulam Stability of the First-Order Difference Equation
We prove Hyers-Ulam stability of the first-order difference equation of the form xi+1=F(i,xi), where F is a given function with some moderate features. Moreover, we introduce some conditions for the function F under which the difference equation is not stable in the sense of Hyers and Ulam.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2016-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2016/6078298 |
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| _version_ | 1832558281382428672 |
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| author | Soon-Mo Jung Young Woo Nam |
| author_facet | Soon-Mo Jung Young Woo Nam |
| author_sort | Soon-Mo Jung |
| collection | DOAJ |
| description | We prove Hyers-Ulam stability of the first-order difference equation of the form xi+1=F(i,xi), where F is a given function with some moderate features. Moreover, we introduce some conditions for the function F under which the difference equation is not stable in the sense of Hyers and Ulam. |
| format | Article |
| id | doaj-art-e6d0cb55488145448e9ab0dbe3d117b5 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-e6d0cb55488145448e9ab0dbe3d117b52025-02-03T01:32:46ZengWileyJournal of Function Spaces2314-88962314-88882016-01-01201610.1155/2016/60782986078298On the Hyers-Ulam Stability of the First-Order Difference EquationSoon-Mo Jung0Young Woo Nam1Mathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Republic of KoreaMathematics Section, College of Science and Technology, Hongik University, Sejong 30016, Republic of KoreaWe prove Hyers-Ulam stability of the first-order difference equation of the form xi+1=F(i,xi), where F is a given function with some moderate features. Moreover, we introduce some conditions for the function F under which the difference equation is not stable in the sense of Hyers and Ulam.http://dx.doi.org/10.1155/2016/6078298 |
| spellingShingle | Soon-Mo Jung Young Woo Nam On the Hyers-Ulam Stability of the First-Order Difference Equation Journal of Function Spaces |
| title | On the Hyers-Ulam Stability of the First-Order Difference Equation |
| title_full | On the Hyers-Ulam Stability of the First-Order Difference Equation |
| title_fullStr | On the Hyers-Ulam Stability of the First-Order Difference Equation |
| title_full_unstemmed | On the Hyers-Ulam Stability of the First-Order Difference Equation |
| title_short | On the Hyers-Ulam Stability of the First-Order Difference Equation |
| title_sort | on the hyers ulam stability of the first order difference equation |
| url | http://dx.doi.org/10.1155/2016/6078298 |
| work_keys_str_mv | AT soonmojung onthehyersulamstabilityofthefirstorderdifferenceequation AT youngwoonam onthehyersulamstabilityofthefirstorderdifferenceequation |