Hyers–Ulam Stability for Quantum Equations of Euler Type
Many applications using discrete dynamics employ either q-difference equations or h-difference equations. In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (q-difference) equation of Euler type. In particular, we show a direct connection between quantum equations of Eu...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/5626481 |
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| _version_ | 1832568167096909824 |
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| author | Douglas R. Anderson Masakazu Onitsuka |
| author_facet | Douglas R. Anderson Masakazu Onitsuka |
| author_sort | Douglas R. Anderson |
| collection | DOAJ |
| description | Many applications using discrete dynamics employ either q-difference equations or h-difference equations. In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (q-difference) equation of Euler type. In particular, we show a direct connection between quantum equations of Euler type and h-difference equations of constant step size h with constant coefficients and an arbitrary integer order. For equation orders greater than two, the h-difference results extend first-order and second-order results found in the literature, and the Euler-type q-difference results are completely novel for any order. In many cases, the best HUS constant is found. |
| format | Article |
| id | doaj-art-b6c7565c1aab432a892ac61b88ff9cfe |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b6c7565c1aab432a892ac61b88ff9cfe2025-02-03T00:59:42ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/56264815626481Hyers–Ulam Stability for Quantum Equations of Euler TypeDouglas R. Anderson0Masakazu Onitsuka1Department of Mathematics, Concordia College, Moorhead, MN 56562, USAOkayama University of Science, Department of Applied Mathematics, Okayama 700-0005, JapanMany applications using discrete dynamics employ either q-difference equations or h-difference equations. In this work, we introduce and study the Hyers–Ulam stability (HUS) of a quantum (q-difference) equation of Euler type. In particular, we show a direct connection between quantum equations of Euler type and h-difference equations of constant step size h with constant coefficients and an arbitrary integer order. For equation orders greater than two, the h-difference results extend first-order and second-order results found in the literature, and the Euler-type q-difference results are completely novel for any order. In many cases, the best HUS constant is found.http://dx.doi.org/10.1155/2020/5626481 |
| spellingShingle | Douglas R. Anderson Masakazu Onitsuka Hyers–Ulam Stability for Quantum Equations of Euler Type Discrete Dynamics in Nature and Society |
| title | Hyers–Ulam Stability for Quantum Equations of Euler Type |
| title_full | Hyers–Ulam Stability for Quantum Equations of Euler Type |
| title_fullStr | Hyers–Ulam Stability for Quantum Equations of Euler Type |
| title_full_unstemmed | Hyers–Ulam Stability for Quantum Equations of Euler Type |
| title_short | Hyers–Ulam Stability for Quantum Equations of Euler Type |
| title_sort | hyers ulam stability for quantum equations of euler type |
| url | http://dx.doi.org/10.1155/2020/5626481 |
| work_keys_str_mv | AT douglasranderson hyersulamstabilityforquantumequationsofeulertype AT masakazuonitsuka hyersulamstabilityforquantumequationsofeulertype |